long range spatial correlations for anisotropic zero range processes the spatial correlations are investigated for a homogeneous system of indistinguishable particles undergoing stochastic anisotropic hopping dynamics on the d dimensional lattice d or 2 the interaction is zero range i e the rate at which particles leave a given site only depends on the occupation number at that site a series expansion around the independent particle system is given for the equal time correlations and is shown to converge for small times t the formal t to infinity limiting expansion is analysed termwise from which a quadrupole type decay approximately r d is derived for the stationary two points function eta 0 eta r eta 0 2 this phenomenon of self organized criticality is a direct consequence of the anisotropy causing the system to violate the condition of detailed balance combined with the conservation law forcing a diffusive decay approximately t d2 of the temporal correlations

a monte carlo method for series expansions the authors describe a simple and general algorithm to calculate series expansions in enumeration problems to large orders approximately by a monte carlo method it can be used to generate unbiased samples in cluster studies e g linear or branched polymers random surfaces etc in any dimension they calculate the number of site animals of size n on the square lattice for n or 50 and their average size to better than 1 accuracy

finite size scaling and universality in the spectrum of the quantum ising chain i periodic and antiperiodic boundary condition the spectrum of the quantum ising chain is studied in the finite size scaling limit for periodic and antiperiodic boundary conditions the finite size corrections are computed for all energy gaps the results of the model are used to test the privman fisher universality hypothesis and conformal theory at the critical point it is shown how to build the spectrum from the irreducible representations of the virasoro algebra in addition the author finds evidence for an unsuspected symmetry for systems both non critical and of finite size

critical exponents of self avoiding walks on a family of truncated n simplex lattices the authors have studied self avoiding walks saws on a family of truncated n simplex lattices which provide a family of fractals in which the fractal dimension d can be varied to a wide range while the spectral dimension d is held almost fixed by means of exact renormalisation group transformations they have calculated the critical exponents nu alpha and gamma and the connectivity constant mu of the saws for n 5 and 6 they propose an approximate theory for calculating the critical exponents of the saws on fractals which is expected to be accurate at large values of n they show that the theory gives results which are in good agreement with exact values even for small values of n and leads to simple closed relations for the exponents

persistency of two dimensional self avoiding walks the authors investigate the persistency of self avoiding walks on the square lattice by studying the distribution of endpoint displacements projected in the direction of the first step exact enumeration and the constant fugacity monte carlo data indicate that the mean displacement after n steps xn increases logarithmically with n while the higher odd moments x2k 1n vary as n2kv in n where v is the correlation length exponent this unusual behaviour for the moments is found to arise from a simple scaling behaviour of the asymmetric component of the displacement distribution which in the constant fugacity ensemble can be written in the form a x approximately n 2v in n exp bx nv where n is the average number of steps in the walk at a fixed value of the fugacity and b is a coefficient of order unity

pair correlations in the antiperiodic ising strip and conformal invariance an explicit formula for the spatial dependence of the pair correlation function in an ising strip with antiperiodic boundary conditions at the bulk critical temperature is given it follows from the conformal invariance approach of belevin et al 1986 and cardy 1986

tricriticality and persistency of trails and silhouettes trails and silhouettes polymers with loops are generated using exact enumeration on a face centred cubic lattice by assigning a tunable fugacity factor with each intersection it is observed that as the fugacity for intersections is increased the trail and silhouette configurations change from swollen to compact ones indicating the existence of tricritical points strong divergence of the specific heats for different path lengths is used to locate these tricritical points the dlog pade scheme is used to compute the corresponding tricritical exponents in the limit of large path lengths the tricritical exponents thus obtained show that these tricritical points are distinct from the usual theta point and that trails and silhouettes do not belong to the saw universality class the tricritical exponents further show that trails and silhouettes do not belong to the same universality class persistency arising from fixing the initial step is also investigated and it is found that odd moments of the persistency obey a power law that can be expressed in terms of the critical exponent nu and the path length l

monte carlo study of random walks on a 2d gasket fractal in an external field using monte carlo simulation random walks on a two dimensional sierpinski gasket in the presence of an external field were studied it was observed that the random walk motion of a particle displayed a crossover from anomalous diffusion to drift for a non zero bias field and the crossover time tcr was a decreasing function of the external bias field the associated dynamic exponents obtained in a computer simulation agree with the predictions of stinchcombe s scaling treatment 1985

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

critical behaviour of a surface reaction model with infinitely many absorbing states in a recent letter yaldram et al 1993 studied the critical behaviour of a simple lattice gas model of the co no catalytic reaction the model exhibits a second order non equilibrium phase transition from an active state into one out of infinitely many absorbing states estimates for the critical exponent beta suggested that the model belongs to a new universality class the results reported in this article contradict this notion as estimates for various critical exponents show that the model belongs to the universality class of directed percolation

winding angle distribution for planar random walk polymer ring entangled with an obstacle and all that spitzer edwards prager frisch model revisited using a general green function formulation we re derive both i spitzer and his followers results for the winding angle distribution of the planar brownian motion and ii edwards prager frisch results on the statistical mechanics of a ring polymer entangled with a straight bar in the statistical mechanics part we consider both cases of quenched and annealed topology among new results we compute exactly the expectation value of the surface area of the locus of points such that each of them has linking number n with a given closed random walk trajectory ring polymer we also consider the generalizations of the problem for the finite diameter disc like obstacle and winding within a cavity

low lying excitations in the square triangle random tiling model we consider the sub dominant eigenstates of the transfer matrix for the square triangle random tiling model on an infinite strip of width l a numerical algorithm for generation of the corresponding solution of the bethe ansatz is developed numerical finite size scaling analysis of the associated eigenvalues reveals the presence of both integer and non integer critical exponents the analytical value of one of the non integer exponents is found it is also shown numerically that along with the leading correction to the free energy density for some excitations there is a term proportional to

finite size scaling in strips antiperiodic boundary conditions the exact values of the universal amplitude a relating the correlation length xi approximately l a to the strip width l at the critical point of ising and 3 state potts models are obtained for the case of antiperiodic or twisted boundary conditions predictions are also made for the finite size scaling behaviour of the interfacial tension

series expansions of the percolation probability for directed square and honeycomb lattices we have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices for the square bond problem we have extended the series from 41 terms to 54 for the square site problem from 16 terms to 37 and for the honeycomb bond problem from 13 terms to 36 analysis of the series clearly shows that the critical exponent beta is the same for all the problems confirming expectations of universality for the critical probability and exponent we find in the square bond case qc 0 3552994 or 0 0000010 beta 0 27643 or 0 00010 in the square site case qc 0 294515 or 0 000005 beta 0 2763 or 0 0003 and in the honeycomb bond case qc 0 177143 or 0 000002 beta 0 2763 or 0 0002 in addition we have obtained accurate estimates for the critical amplitudes in all cases we find that the leading correction to scaling term is analytic i e the confluent exponent delta 1

small deviations from local equilibrium for a process which exhibits hydrodynamical behavior i the symmetric simple exclusion process on with sources at l l e is considered the stationary measure l is studied in the limit asl diverges the first order correction to its limit is proven to be of order 1 l and it is explicitly computed the result is in agreement with the analysis of the model from the hydrodynamical point of view initiated in ref 1

the ashkin teller quantum chain and conformal invariance the authors study the finite size effects for the fourth state one dimensional quantum chain introduced by kohmoto et al 1981 using different boundary conditions from the corrections to the ground state energy for periodic boundary conditions they verify that the central charge of the virasoro algebra is equal to one in the whole domain of criticality their numerical study suggests a new relation between the corrections to the ground state energy with free boundary conditions and with periodic boundary conditions various critical exponents including the surface ones and those corresponding to the para fermions are determined

finite size scaling for directed bond percolation with and without cycles on a triangular lattice the authors apply finite size scaling and phenomenological renormalisation group arguments to the problems of directed acyclic directed cyclic and undirected bond percolation on a triangular lattice the results are in good agreement with known estimates and show that the phenomenological renormalisation procedure is sensitive to the difference between global and local directional biases as well as the distinction between locally directed and fully isotropic problems in addition the authors draw tentative comments on the extension to directed problems of the relation a pi eta where a is the inverse correlation length amplitude of a strip of finite width at criticality and eta is the exponent that describes the decay of correlations at the critical point known to hold for various isotropic systems

statistical mechanics of non intersecting line systems statistical assemblies of non intersecting closed lines loops with a variable loop multiplicity are considered which may have relevance for defect models of certain phase transitions a loop gas model on a lattice is formulated and shown to be formally equivalent to an m anisotropic n vector model in the limit n 0 in two dimensions the equivalence with the eight vertex model in a field is discussed in a few special cases the novel model is equivalent to known ones

multicriticality in a self dual potts model the authors explore the self dual plane of a two dimensional potts model with vacancies and four spin interactions using finite size scaling of transfer matrix results since the transfer matrix construction is based on the random cluster representation of the potts model its application is not restricted to an integer number q of potts states for q or 4 the self dual plane contains a critical region belonging to the ordinary potts universality class and a region of first order transition points the two regions are separated by a line of which a range consists of potts tricritical points while another range is of a first order nature the point separating these two ranges is for 0 q or 9 4 identified with the multicritical point of which an exact solution has recently been given by nienhuis et al 1979

finite size effects on the critical structure factor of the two dimensional ising model explicit calculations of the critical structure factor of the planar ising model on square lattices with a variety of boundaries are compared with the results of conformal invariance monte carlo methods are used for square circular and 2 1 rectangular geometries with free boundary conditions transfer matrices are used for an infinite strip with periodic boundary conditions good agreement is found for wavevectors less than a quarter of a reciprocal lattice spacing

the geometrical properties of planar lattice trails the authors investigate the winding angle and mean square end to end distance of lattice trails on a square lattice by both exact enumeration and monte carlo methods they find similar behaviour to that of self avoiding walks to the extent that the complete distribution is found to agree with the recent exact calculation of the winding angle distribution function for self avoiding walks by duplantier and saleur 1988 who found a gaussian distribution the exponent nu was found to be indistinguishable from 3 4

operator dimensions and surface exponents for the non linear schrodinger model at t 0 using the euler maclaurin formula the authors compute finite size corrections to the ground and excited state energies and momenta this enables them to obtain all possible operator scaling dimensions at the critical point t 0 and surface exponents for a variety of boundary conditions they extend the predictions of conformal invariance to include green functions with oscillating terms

finite size effects at 2d ising critical points via conformal mapping using recent results by cardy 1984 based on conformal invariance of critical correlation functions the authors calculate universal results for scattering functions s k susceptibilities correlation lengths and specific heat correction terms for finite ising systems in two dimensions with circular elliptical and rectangular shapes and free boundary conditions results show the effects of critical order on these quantities for a circle s k decays as 1 k2 eta for a large range of intermediate k values with an apparent exponent eta 0 09 the probable influence of end edge and domain wall effects in the rectangular geometry is discussed application of the results to experimental systems and other theoretical models is discussed

semi inhomogeneous solutions of the kac model of boltzmann equations constructs semi inhomogeneous solutions of the kac model for which the spatial dependence is only present in the odd velocity part of the distribution at the macroscopic level the local density the local energy and the associated current components are determined and discussed while at the microscopic level there exist two different classes of distributions as an illustration the author gives two solutions explicitly for one class the distributions relax towards a maxwellian equilibrium solution and they correspond either to a contraction or an expansion while for the other they go to zero when the time increases to infinity the space variable appears linearly and in order to maintain the positivity stays inside a finite interval assuming that the distributions are zero outside such intervals a physical interpretation can be obtained for the whole space axis provided appropriate elastic walls sinks and sources are introduced these boundary conditions seem more natural for the class of distributions with maxwellian relaxation

criticality of the discrete n vector ferromagnet in planar self dual lattices the authors study an extended version of the discrete n vector or cubic ferromagnetic model within a real space renormalisation group approach which preserves the two spin correlation function the n evolution for real values of n of the wheatstone bridge hierarchical lattice phase diagram which presents paramagnetic intermediate nematic like and ferromagnetic phases as well as of the thermal nu and crossover phi critical exponents is presented the self avoiding walk problem is recovered in the n to o limit and the so called corner rule is re obtained in a larger context the ising n and 2n state potts ferromagnets are recovered as particular cases an interchange of stability occurs at n n approximately 6 9 in such a way that the 2n state potts special point where all three existing phases join is multicritical if n n but only critical if n n consistently phi n o for the cubic model nu n presents a maximum at n nmax approximately 1 5 the results are exact for all n for the wheatstone bridge hierarchical lattice and approximate for n or 2 for the square lattice last but not least they discuss the connection between the present approach and the phenomenological renormalisation group

on the relation of kinetic gelation and percolation we analyse the results of kinetic gelation and propose a diagram compatible with the existing data we introduce the concept of limited and full universality the former refers to systems with an identical subset of critical exponents the latter refers to systems with an identical set of critical exponents the evidence suggests that kinetic gelation and random percolation are in the same limited universality class it appears that the concentration of initiators plays the role of an active parameter similar to that of the interplane coupling in quasi two dimensional king models

logarithmic corrections in the two dimensional ising model in a random surface field in the two dimensional ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point we study this question by extensive monte carlo simulations for various strengths of disorder the calculated effective temperature or size dependent critical exponents fit with the field theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system s critical behaviour

spiral growing self avoiding walk a new universality class the author introduces the concept of a spiral growing self avoiding walk sgsaw by imposing privman s spiralling constraint ibid vol 16 p l571 1983 on the growing self avoiding walk introduced by majid et al phys rev lett vol 52 p 1257 1984 and lyklema and kremer ibid vol 17 p l691 1984 he studies the critical properties of the sgsaw using monte carlo simulation the exponent nu associated with the average radius of gyration sn is 0 8 on the other hand the critical exponent nu r associated with the end to end distance rn is much less than nu the latter is in sharp contrast to the result nu nu r for the usual saw directed gsaws are shown to behave like directed usual saws

two dimensional o n model in a staggered field nienhuis truncated o n model gives rise to a model of self avoiding loops on the hexagonal lattice each loop having a fugacity of n we study such loops subjected to a particular kind of staggered field w which for n has the geometrical effect of breaking the three phase coexistence linked to the three colourability of the lattice faces we show that at t 0 for w 1 the model flows to the ferromagnetic potts model with q n2 states with an associated fragmentation of the target space of the coulomb gas for t 0 there is a competition between t and w which gives rise to multicritical versions of the dense and dilute loop universality classes via an exact mapping and numerical results we establish that the latter two critical branches coincide with those found earlier in the o n model on the triangular lattice using transfer matrix studies we have found the renormalization group flows in the full phase diagram in the t w plane with fixed n superposing three copies of such hexagonal lattice loop models with staggered fields produces a variety of one or three species fully packed loop models on the triangular lattice with certain geometrical constraints possessing integer central charges 0 c 6 in particular we show that benjamini and schramm s rgb loops have fractal dimension df 3 2

computer simulation of a model for irreversible gelation a random mixture of bifunctional and tetrafunctional units is placed on a simple cubic lattice permanent bonds between these units are then formed by the random motion of active centres radicals resulting in a model for the gelation of polyacrylamide and similar processes the largest of the clusters formed by this kinetic percolation process is identified with the gel fraction the mean cluster size with the weight average degree of polymerisation the critical exponent gamma of the mean cluster size is roughly the same as for random percolation that is different from that of the classical theory of flory 1941 and stockmayer 1943 but the corresponding amplitude ratio that is the ratio of average molecular weight on both sides of the gel point differs strongly from its value in random percolation thus this kinetic gelation model seems to belong to a universality class of its own different from both that of random percolation and that of classical gelation theories

manhattan lattice theta point exponents from kinetic growth walks and exact results from the nienhuis o n model kinetic growth walks kgw on the manhattan lattice have previously been shown to be equivalent to the static problem of interacting self avoiding walks on that lattice at the theta temperature here we illustrate how a complete set of exponents for the static problem including the crossover exponent phi and surface exponents at the ordinary and special transition points may be obtained from simulations of kinetic walks in the process we find that phi m 0 430 or 0 006 which encompasses the conjectured value 3 7 approximately 0 42857 for the theta point on an isotropic lattice our numerics confirm a predicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk transition furthermore we point out that a recently examined variant of the nienhuis o n model can be mapped onto theta point walks on the manhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the numerical conjectures

persistency studies of trails and silhouettes on square and triangular lattices the authors study the persistencies of trails and silhouettes on two dimensional square and triangular lattices these persistencies are induces by fixing the first step of the walk in the positive x direction trails are walks which are not allowed to overlap on themselves but may self intersect whereas silhouettes are just the shadows of trails associated with each self intersection is an attractive interaction energy epsilon mod epsilon mod thus a fugacity factor f i theta theta eitkbt ei theta where i is the number of intersections may be defined this has the advantage of providing a handle on the temperature and such dependence of persistencies on temperature is studied for the first time in this paper they are found to obey a law that may be expressed as a function of the critical exponents x2k 1l theta approximately lpk nu theta f l where l is the chain length nu is the correlation exponent f l approximately loge l or some weak function of l e g lw where w 1 0 p is a parameter and k 0 1 2

persistency properties of models of polymers on simple cubic and face centred cubic lattices the first four odd moments of the persistence lengths of trails and silhouettes are studied on two different 3d lattices the simple cubic lattice and the face centred cubic lattice variations of the averaged persistence lengths with chain lengths l and inverse temperatures theta are systematically examined it is found that the averaged persistence lengths scale with a scaling law of the form xl2k 1 theta approximately lpk nu theta f l where nu is the correlation exponent p is a parameter k 0 1 2 and f l approximately constant in contrast to the results in 2d where f l approximately loge l

stationary states for a mechanical system with stochastic boundary conditions we consider a system of newtonian particles with a long range repulsive pair potential moving in a cavity whose surface temperature is spatially varying when a particle hits the surface it is thermalized at the temperature of the collision point we prove that this system has a unique stationary ensemble to which any initial distribution converges for large times we show that this stationary ensemble depends continuously on the surface temperature profile

a monte carlo renormalisation group for aggregation processes a general monte carlo renormalisation group transformation for the static as well as the kinetic properties of aggregates is formulated and applied to different growth models particle aggregation dla cluster aggregation cici and invasion percolation ip the leading critical exponent is determined numerically for dla the first correction to scaling exponent has been estimated as well

marginal extended perturbations in two dimensions and gap exponent relations the most general form of a marginal extended perturbation in a two dimensional system is deduced from scaling considerations it includes as particular cases extended perturbations decaying either from a surface a line or a point for which exact results have been previously obtained the first order corrections to the local exponents which are functions of the amplitude of the defect are deduced from a perturbation expansion of the two point correlation functions assuming covariance under conformal transformation the perturbed system is mapped onto a cylinder working in the hamiltonian limit the first order corrections to the lowest gaps are calculated for the ising model the results confirm the validity of the gap exponent relations for the perturbed system

anomalous diffusion on regular and random models for diffusion limited aggregation families of regular fractal models for witten sander dla clusters in d dimensions are proposed resembling the computer generated aggregates the authors evaluate random walk dimensionalities exactly using resistance scaling ideas the applicability of the conflicting conjectures of alexander orbach 1982 ao dw 3df 2 and aharony stauffer 1984 as dw df 1 to dla is then examined one finds that the dendritic nature of the fractals presented ensures that as is satisfied exactly in all dimensions an rsrg fugacity transformation method is applied to the simplest of the regular fractals in d 2 the result for dw is compared with the exact resistance scaling result to obtain an estimate of the error introduced by the rsrg the rg method is then generalised to treat the random dla problem the resulting estimate for dw is in fortuitously good agreement with as the corresponding monte carlo data and the results above for the regular fractal models

critical behaviour of two interacting linear polymer chains exact results for a state of interpenetration of chains on a fractal lattice a model of two interacting chemically different linear polymer chains on a fractal lattice is proposed to study segregation and interpenetration of chains using the real space renormalization group transformation the value of the contact exponent at the point of the interpenetration transition is calculated exactly for the 2d sierpinski gasket

critical properties of the spin 1 2 heisenberg chain with frustration and bond alternation we study the heisenberg chain with frustration and alternation which is expressed by both analytically and numerically we focus on the case where there is no marginal operator which brings about the logarithmic corrections in various quantities by using the bosonization method we calculate the energy gap the change in the ground state energy due to the alternation so called energy gain the spin correlation and the string correlation not only their exponents but also their amplitudes and compare them with the results of the numerical diagonalization for finite systems we point out the existence of the logarithmic correction in the energy gain despite the absence of the marginal operator taking into account this logarithmic correction we can obtain a reasonable hyperscaling relation between the critical exponents of the energy gap and an energy gain from the numerical data

the generalised true self avoiding walk a model with continuously variable exponent ν the true self avoiding walk is generalised by admitting that the self avoidance parameter depends on the past history of the walk for the generalised model the end to end distance exponent nu is calculated by a method that gives the same result as a flory type theory for the usual true self avoiding walk the exponent nu is predicted to be continuously variable with one of the parameters of the generalised model the resulting expression for the exponent nu is confirmed by monte carlo simulations

critical behaviour in parabolic geometries the authors study two dimensional systems with boundary curves described by power laws using conformal mappings they obtain the correlations at the bulk critical point three different classes of behaviour are found and explained by scaling arguments which also apply to higher dimensions for an ising system of parabolic shape the behaviour of the order at the tip is also found

finite size corrections for ground states of the xxz heisenberg chain the method of de vega and woynarovitch 1985 is used to calculate finite size corrections to the ground state energy in different sectors for the xxz heisenberg chain finite size scaling amplitudes and correction to scaling exponents in the critical region are derived using conformal invariance a scaling dimension x pi gamma 2 pi is extracted corresponding to the electric field operator in the 8 vertex model this confirms a conjecture of baxter and kelland 1974 finite size scaling properties near the kosterlitz thouless critical point delta 1 are discussed

a unifying model of generalised random walks the authors propose a unifying model for generalised static random walks in which each walk has a weight exp g sigma ni alpha where ni is the occupation number of a site and alpha and g are variable parameters special cases of this general walk include the ordinary brownian random walk the self avoiding walk the lattice domb joyce model 1972 and the interacting random walk model recently introduced by stanley et al 1983 the asymptotic properties of the walk are studied in one dimension by effective medium arguments and exact enumeration methods for repulsive correlations the authors find saw behaviour while for attractive correlations the model is self trapping for 1 alpha or 2 and exhibits anomalous diffusion with continuously varying exponents for 0 or alpha 1 in higher dimensions comments are made about effective medium predictions and their relationship to other generalised random walk models

phase transitions in two dimensional stochastic cellular automata two dimensional stochastic cellular automata with nearest neighbour couplings are investigated depending on the rules low level noise phases are classified into ferro glassy roll glassy roll and antiferro glassy antiferro antiferro roll glassy antiferro roll coexistent phase of ferro and antiferro labyrinth and turbulence also the oscillating phases with period 2 for the above phases are observed in other rules transformations from ferro to antiferro and from fixed point to periodic patterns are shown the nature of phase transitions due to a change of noise is investigated

a new type of kinetic critical phenomenon the authors study a new critical phenomenon in an non thermal one dimensional lattice model it is characterised by the transition from stability to instability of kinks between ordered states below the critical point the kinks are stable and move by annihilating random walks above the critical point they are unstable against creation of kink antikink pairs the spontaneous production of pairs is assumed to be absent at the critical point p pcr the density of kinks decreases like n approximately talpha with alpha 0 27 or 0 08 above the critical point the density of kinks in the stationary state is approximately p pcr beta with beta 0 06 or 0 2 possible extensions to two or more dimensions and possible applications are discussed

some further results on a kinetic critical phenomenon a critical cluster growth phenomenon is studied in which the number of particles is locally conserved modulo 2 this puts it in a new universality class although the process is superficially similar to directed percolation the author gives much improved values for the critical exponents in one dimension and presents first attempts towards a field theoretic description

the dynamic critical exponent of the q 3 and 4 state potts model the dynamic monte carlo renormalisation group method introduced by jan moseley and stauffer 1983 is used to determine the dynamic critical exponent z for the q 3 and q 4 state potts model in two dimensions the authors find that z 2 43 or 0 15 and 2 36 or 0 20 for the q 3 and q 4 state potts models these results are in disagreement with the recent conjecture of domany 1984

scaling and critical probabilities for cluster size and la diversity on randomly occupied square lattices using monte carlo simulations we report the behaviour of the total number of clusters the cluster size diversity and the lattice animals la diversity on randomly occupied square lattices the critical probability associated with the maximum of these variables is determined in comparison with the percolation probability pc our simulations indicate that pc and the critical probability of the maximum cluster size diversity pc d s max occur at the same point as indicated in a previous paper tsang i r and tsang i j 1997 j phys a math gen 30 l239 the probability for the maximum number of clusters is obtained at a lower value pc n max 0 27 0 01 we describe the cluster identification algorithm used to count the different la and determined the critical probability for the maximum la diversity pc d f max 0 45 0 02 we derive the exponents characterizing the relation between d s max d f max and n max and several scaling relations between the variables measured the lattice size and the probability of occupation p in addition we show the scaling behaviour of la diversity versus cluster size diversity for each value of p

exact relations between kinetic gelation and percolation an exact relation between one of the recently introduced models for kinetic gelation and random percolation is displayed this explains the frequently observed identity between the exponents of the two models moreover it strongly suggests that any further universal properties of percolation are also shared by kinetic gelation in particular a rigorous inequality due to van den berg and kesten 1985 can be used to display an inconsistency between the observed values of the exponents beta and nu and the observed value of the fractal dimension of the backbone in kinetic gelation the more complex issue of the observed variation of the amplitude ratio cannot be easily resolved however should the observed discrepancies be real they would according to the author s results indicate that the amplitude ratio can indeed vary depending upon the underlying lattice structure

a cluster cluster aggregation model with tunable fractal dimension a hierarchical cluster cluster aggregation computer model is introduced which allows one to build random fractal aggregates on a d dimensional lattice with a fractal dimension fixed a priori the algorithm works iteratively by sticking aggregates of the same number of particles at the correct centre to centre distance in order to recover the desired scaling with the more efficient versions of the model any fractal dimension ranging from 1 up to a d dependent upper limit dm d can be obtained one estimates dm 2 approximately 1 80 or 0 03 and dm 3 approximately 2 55 or 0 04 calculations up to d 8 show that the ratio dm d d decreases as d increases

non perturbative tricritical exponents of trails ii exact enumerations on square and simple cubic lattices for pt i see ibid vol 21 p 773 1988 the authors present exact enumerations of trails self intersecting but non overlapping lattice walks tabulated according to their length l number of intersection i and end to end distance for the square lattice up to l 21 i 7 and for the simple cubic lattice up to l 15 i 5 they introduce a fugacity for intersection to explore the transition to a collapsed phase through a novel tricritical point which is unaccessible by the renormalisation group approach the existence of tricritical points in both lattices is manifested by the divergence of the specific heat the values of the tricritical couplings and exponents are extracted by a dlogpade analysis they find for the three dimensional lattice nu t approximately 0 48 and gamma t approximately 0 43 nu t approximately 0 52 and gamma t approximately 1 25 for the square lattice

ballistic chain chain aggregation in d 1 3 the on lattice ballistic chain chain aggregation model is studied by monte carlo simulations in one two and three dimensions the chains move along the lattice directions with a velocity proportional to kgamma for a k mer the fractal dimension of the large polymers and the mass distribution are computed for different values of the mobility exponent gamma in two and three dimensions a long preasymptotic behaviour is observed and in all dimensions the asymptotic behaviour is in agreement with the smoluchowski theory

branching annihilating random walks in one dimension some exact results we derive a self duality relation for a one dimensional model of branching and annihilating random walkers with an even number of offspring on nearest neighbour sites with the duality relation and by deriving further exact results in some limiting cases involving fast diffusion we obtain new information on the location and nature of the phase transition line between an active stationary state non zero density and an absorbing state extinction of all particles thus clarifying some so far open problems in these limits the transition is mean field like but on the active side of the phase transition line the fluctuation in the number of particles deviates from its mean field value we also show that well within the active region of the phase diagram a finite system approaches the absorbing state very slowly on a time scale which diverges exponentially in system size in the absence of particle diffusion the branching process with infinite annihilation rate is strongly non ergodic

the dimer trimer model for heterogeneous catalysis a new universality class the authors study a new model for heterogeneous catalysis in which dimers a2 and trimers b3 are chemisorbed onto a triangular lattice nearest adsorbed a and b neighbours react and desorb leaving behind two empty sites they observe a phase diagram similar to that of the monomer dimer model of ziff gulari and barshad 1986 with a stationary reactive phase in between a dimer poisoned and a trimer poisoned phase there is a first order transition from the reactive phase to the dimer poisoned phase and a second order transition to the trimer poisoned phase however the second order transition is in a different universality class from reggeon field theory in contrast to all previously studied models for catalysis the difference stems from the infinite number of absorbing states in the trimer poisoned phase special to their model

finite size scaling and conformal invariance in a self dual quantum z 5 model considers the critical behaviour of a particular set of onedimensional self dual models with z n symmetry n or 5 the critical indices are evaluated using standard finite size scaling and by exploiting their relations with the mass gap amplitudes predicted by conformal invariance the results strongly suggest that the recently introduced z n quantum field theory is the underlying field theory for these statistical mechanics models

the number of incipient spanning clusters in two dimensional percolation using methods of conformal field theory we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k i n the limit when k is large the study of the structure of large clusters at the percolation threshold continues to pose interesting problems whose solution sheds light on the nature of the critical state in general recently some attention has been paid to incipient spanning clusters iscs these are clusters which connect two disjoint segments of the boundary of a macroscopically large region langlands et al 1 conjectured that the probability that at least one such cluster exists that is that the segments are connected is invariant under conformal transformations this statement was placed in the context of conformal field theory in 2 where an explicit formula was given for this crossing probability for a review of the status of conformal invariance in critical percolation see 3 more recently aizenman 4 has considered among other things the probability that there exist n distinct iscs connecting the two segmentsy in the case of a rectangular region 0 kl 0 l he has proved that the probability p n k l that the strip is traversed in the direction of length kl b y nindependent clusters satisfies the bounds a e n 2 k

a novel growing self avoiding walk in three dimensions the authors introduce a growing self avoiding walk in three dimensions 3d that can terminate only by returning to its point of origin this symmetric tricolour walk stw is a direct generalization of the smart kinetic walk to 3d and yet is readily simulated their monte carlo simulations strongly suggest that the fractal dimension of the stw is exactly 2 this conclusion is supported by a mapping of the stw onto a self attracting self avoiding walk at its collapse transition

amplitude exponent relation for the correlation length in the spherical model for the critical spherical model in d r 1 dimensions finite size calculations of the spin spin and energy energy correlation lengths suggest relations among the critical exponents and the finite size scaling amplitudes of the correlation lengths similar to those obtained in 1 1 dimensions from conformal invariance for antiperiodic boundary conditions the results agree with numerical studies in the 2 1 dimensional ising model

critical exponents for a dimer dimer irreversible surface reaction abstract a dimer dimer reaction model of the type a2 b2 2ab is investigated by means of computer simulations the desorption of b2 dimer with probability p is studied here we investigate the critical behaviour the critical exponents of our model do not fall into the reggeon field theory or directed percolation universality class the universality class of the reaction changes with changes in p

hitting times for special patterns in the symmetric exclusion process on z d we consider the symmetric exclusion process eta t t 0 on 0 1 z d we fix a pattern a eta sum lambda eta i ge k where lambda is a finite subset of z d and k is an integer and we consider the problem of establishing sharp estimates for tau the hitting time of a we present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for tau in a simple way also we characterize the trajectories eta s s le t conditioned on tau t

test of finite size scaling predictions in three dimensions a constrained monomer dimer cmd model on decorated hypercubic lattices which is exactly solvable in any dimensionality d is studied the model is critical in the limit of maximal packing of the dimer configurations allowed by the constraint for d 2 it is equivalent to the rooted tree model on the square lattice considered by duplantier and david 1988 the validity of two finite size scaling predictions in higher dimensionalities is studied 1 the existence of logarithmic corrections in the free energy due to corners and ii the amplitude exponent relation for the pair correlation function the logarithmic finite size corrections are obtained for arbitrary d for boundary conditions which are periodic for d or 0 dimensions and free in the remaining d d dimensions dimer dimer correlation functions are studied at d 3 for a system finite in two dimensions and infinite in the third it is shown that the amplitude exponent relation for the cmd model holds for d 2 and breaks down for d 3

true self avoiding walks on fractal lattices above the upper marginal dimension we study by monte carlo simulations the critical behaviour and the cross over scaling of the true self avoiding walks tsaw on fractal lattices above the upper marginal dimension we estimate the flory exponent nu which characterizes the rms end to end distances of saw on a percolation cluster at percolation thresholds both in three and four dimensions and on a dla cluster in three dimensions results were in good agreement with the predictions of the known flory formulae we also discuss the fractal to euclidean and the rw to tsaw cross over scaling monte carlo data appear to collapse in the scaling regions for both cases however we found that the scaling function for the latter is different from that on the regular lattices

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

tests of hyperuniversality for self avoiding walks a universal combination of amplitudes for the end to end distance of n step self avoiding walks and for the number of n step self avoiding polygons is estimated numerically for various lattices in d 2 universality of this amplitude combination is confirmed to good accuracy while in d 3 the data are consistent with universality but the error limits are rather large for finite width square lattice strips the authors calculate universal critical point correlation amplitudes by fixed fugacity monte carlo simulations in addition these amplitudes are calculated analytically either exactly or approximately by cardy s conformal mapping approach numerical values agree well with the theoretical predictions

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

critical behaviour and logarithmic corrections of a quantum model with three spin interaction extended finite size scaling and series expansion methods are used to determine the critical properties of the one dimensional quantum ising model with three spin interaction by supposing the presence of logarithmic corrections the universality class of the model is investigated the results obtained by different methods support the conjecture that the model belongs to the same universality class as the four state potts model

are damage spreading transitions generically in the universality class of directed percolation we present numerical evidence for the fact that the damage spreading transition in the domany kinzel automaton found by martinset al is in the same universality class as directed percolation we conjecture that also other damage spreading transitions should be in this universality class unless they coincide with other transitions as in the ising model with glauber dynamics and provided the probability for a locally damaged state to become healed is not zero

a critical amplitude relation for one dimensional quantum transitions and determination of the exponent eta a new critical amplitude relation which holds for one dimensional quantum ground state transitions is presented the relation yields an estimate of the sound velocity which appears in the conformal field theory as an a priori unknown parameter with the use of this relation the exponent eta can be explicitly determined from only the scaling fit of the off critical energy gap the relation is confirmed in the transverse ising model the s 1 2 anisotropic xy model and the three state potts model

microscopic stationary states for stochastic systems with particle flux let t be the symmetric nearest neighbor simple exclusion process on 3 modified to allow the spontaneous creation and destruction of particles at the origin we study the invariant measures for the system in this non equilibrium situation for which a net current of particles flows from the origin we analyze the n point correlations of the invariant measures which for n 2 behave like max x1x2 4

a new class of critical exponents in a dimer monomer catalytic surface reaction the critical behaviour of a dimer monomer bc a to 1 2c2 ab irreversible catalytic surface reaction is investigated by means of monte carlo simulation technique on a hexagonal lattice each site having six nearest neighbours the reaction exhibits a steady reactive state between two critical concentrations ya1 and ya2 of a the critical exponents associated with various order parameters i e coverages at the second order phase transition ya1 have been obtained these exponents do not fall in the universality class of reggeon field theory as is the case of 1 2b2 a to ab the usual dimer monomer reaction