exact amplitude ratio and finite size corrections for the mxn square lattice ising model let f u and c represent respectively the free energy the internal energy and the specific heat of the critical ising model on the mxn square lattice with periodic boundary conditions and f infinity represents f for fixed m n and n infinity we find that f u and c can be written as n f f infinity summation operator infinity i 1 f 2i 1 n 2i 1 u square root of 2 summation operator infinity i 1 u 2i 1 n 2i 1 and c 8 ln n pi summation operator infinity i 0 c i n i i e nf and u are odd functions of n 1 we also find that u 2i 1 c 2i 1 1 square root of 2 and u 2i c 2i 0 for 1 or i infinity and obtain closed form expressions for f u and c up to orders 1 n 5 1 n 5 and 1 n 3 respectively which implies an analytic equation for c 5

tricriticality and the blume capel model a monte carlo study within the microcanonical ensemble the microcanonical partition function ensuremath omega ensuremath alpha n e of a three dimensional ferromagnetic simple cubic blume capel model is calculated for several coupling ratios ensuremath alpha close to and on the first order side of the tricritical point to this end a single monte carlo simulation of a suitably extended partition function for systems of l ifmmode times else texttimes fi l ifmmode times else texttimes fi l spins with l ensuremath in 8 10 12 14 18 was performed a finite system analog of the latent heat is introduced in order to define a tricritical point in finite systems as well an empirical scaling of its coordinates to the thermodynamic limit yields ensuremath alpha t 2 84479 ifmmode pm else textpm fi 0 00030 for the tricritical coupling ratio and k b t t j 1 4182 ifmmode pm else textpm fi 0 0055 for the tricritical transition temperature the results are compared with values obtained on fcc lattices

critical frontier of the potts and percolation models on triangular type and kagome type lattices i closed form expressions we consider the potts model and the related bond site and mixed site bond percolation problems on triangular type and kagome type lattices and derive closed form expressions for the critical frontier for triangular type lattices the critical frontier is known usually derived from a duality consideration in conjunction with the assumption of a unique transition our analysis however is rigorous and based on an established result without the need of a uniqueness assumption thus firmly establishing all derived results for kagome type lattices the exact critical frontier is not known we derive a closed form expression for the potts critical frontier by making use of a homogeneity assumption the closed form expression is unique and we apply it to a host of problems including site bond and mixed site bond percolations on various lattices it yields exact thresholds for site percolation on kagome martini and other lattices and is highly accurate numerically in other applications when compared to numerical determination

percolation transitions in two dimensions we investigate bond and site percolation models on several two dimensional lattices numerically by means of transfer matrix calculations and monte carlo simulations the lattices include the square triangular honeycomb kagome and diced lattices with nearest neighbor bonds and the square lattice with nearest and next nearest neighbor bonds results are presented for the bond percolation thresholds of the kagome and diced lattices and the site percolation thresholds of the square honeycomb and diced lattices we also include the bond and site percolation thresholds for the square lattice with nearest and next nearest neighbor bonds we find that corrections to scaling behave according to the second temperature dimension xt2 4 predicted by the coulomb gas theory and the theory of conformal invariance in several cases there is evidence for an additional term with the same exponent but modified by a logarithmic factor only for the site percolation problem on the triangular lattice does such a logarithmic term appear to be small or absent the amplitude of the power law correction associated with xt2 4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems

on performance congruences for process algebras based on the hypothesis of durational actions and process synchronization with busy waiting mechanism performance equivalencehas been proposed to introduce a simple form of performance evaluation in process algebras this equivalence enjoys many of the pleasant properties of those in the untimed setting but it is not a congruence for parallel composition with synchronization in this paper we give a bisimulation based characterization of the coarsest congruence contained within performance equivalence and discuss alternative formulations this problem was left open in several papers we study how the new equivalence calledperformance congruence relates with other closed equivalences in the literature and show that unlike other proposals it is a natural extension of those standard in the untimed setting the weak version of performance congruence which abstracts from internal details is also studied a number of examples of processes related or taken apart by performance congruence and its weak version are provided a nontrivial one is also presented to illustrate the utility of the new congruences the paper concludes with further observations concerning performance congruence and with a discussion on related and further interesting work

fast monte carlo algorithm for site or bond percolation we describe in detail an efficient algorithm for studying site or bond percolation on any lattice the algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system we demonstrate our algorithm by using it to investigate a number of issues in percolation theory including the position of the percolation transition for site percolation on the square lattice the stretched exponential behavior of spanning probabilities away from the critical point and the size of the giant component for site percolation on random graphs

the critical manifolds of inhomogeneous bond percolation on bow tie and checkerboard lattices we give a conditional derivation of the inhomogeneous critical percolation manifold of the bow tie lattice with five different probabilities a problem that does not appear at first to fall into any known solvable class although our argument is mathematically rigorous only on a region of the manifold we conjecture that the formula is correct over its entire domain and we provide a non rigorous argument for this that employs the negative probability regime of the triangular lattice critical surface we discuss how the rigorous portion of our result substantially broadens the range of lattices in the solvable class to include certain inhomogeneous and asymmetric bow tie lattices and that if it could be put on a firm foundation the negative probability portion of our method would extend this class to many further systems including f y wu s checkerboard formula for the square lattice we conclude by showing that this latter problem can in fact be proved using a recent result of grimmett and manolescu for isoradial graphs lending strong evidence in favor of our other conjectured results this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

universal finite size scaling functions with exact nonuniversal metric factors using exact partition functions and finite size corrections for the ising model on finite square plane triangular and honeycomb lattices and extending a method j phys 19 l1215 1986 to subtract leading singular terms from the free energy we obtain universal finite size scaling functions for the specific heat internal energy and free energy of the ising model on these lattices with exact nonuniversal metric factors

exact solution of smoluchowski s equation for reorientational motion in maier saupe potential abstract the analytic treatment of the non inertial rotational diffusion equation i e of smoluchowski s one se in a symmetric genuinely double well maier saupe uniaxial potential of mean torque is considered such potential may find applications to reorientations of the fragments of structure in polymers and proteins we obtain the exact solution of se via the confluent heun s function the solution is uniformly valid for any barrier height we apply the obtained solution to the calculation of the mean first passage time and the longitudinal correlation time and obtain their precise dependence on the barrier height in the intermediate to high barrier low temperature region the results of our approach are in full agreement with those of the approach developed by coffey kalmykov dejardin and their coauthors in the low barrier high temperature region our results noticeably distinguish from the predictions of the literature formula and give appreciably greater values for the transition rates from the potential well the reason is that the above mentioned formula is obtained in the stationary limit we conclude that for very small barrier heights the transient dynamics plays a crucial role and has to be taken into account explicitly when this requirement is satisfied as e g at the calculation of the longitudinal correlation time we obtain absolute identity of our results with the literature formula in the whole range of barrier heights the drawbacks of our approach are its applicability only to the symmetric potential and its inability to yield an analytical expression for the smallest non vanishing eigenvalue

relaxation dynamics of a particle in the presence of an external potential exact solution in terms of matrix continued fractions exact expressions for the laplace transform of the after effect function arising from the solution of the langevin or underlying fokker planck equation for brownian motion in an external potential are obtained as a sum of products of infinite matrix continued fractions this is accomplished by reducing the scalar multiterm recurrence relations associated with the fokker planck equation to matrix three term recurrence relations the solution is illustrated by considering the problem of dielectric relaxation of a single axis rotator subjected to both constant and crystalline anisotropy fields

site percolation thresholds for archimedean lattices precise thresholds for site percolation on eight archimedean lattices are determined by the hull walk gradient percolation simulation method with the results p c 0 697 043 honeycomb or 6 3 0 807 904 3 12 2 0 747 806 4 6 12 0 729 724 4 8 2 0 579 498 3 4 6 0 621 819 3 4 6 4 0 550 213 3 3 4 2 and 0 550 806 3 2 4 3 4 with errors of about 3 x 10 6 the remaining archimedean lattices are the square 4 4 triangular 3 6 and kagome 3 6 3 6 for which p c is already known exactly or to a high degree of accuracy the numerical result for the 3 12 2 lattice is consistent with the exact value 1 2 sin pi 18 1 2 the values of p c for all 11 archimedean lattices as well as a number of nonuniform lattices are found to be well correlated by a nearly linear function of a generalized scher zallen filling factor this correlation is much more accurate than recently proposed correlations based solely upon coordination number

predictions of bond percolation thresholds for the kagome and archimedean 3 12 2 lattices here we show how the recent exact determination of the bond percolation threshold for the martini lattice can be used to provide approximations to the unsolved kagom e and 3 12 2 lattices we present two different methods one which provides an approximation to the inhomogeneous kagom e and 3 12 2 bond problems and the other which gives estimates of p c for the homogeneous kagom e 0 524 408 8 dots and 3 12 2 0 740 421 2 dots problems that respectively agree with numerical results to five and six significant figures

generalized cell dual cell transformation and exact thresholds for percolation suggested by scullard s recent star triangle relation for correlated bond systems we propose a general cell dual cell transformation which allows in principle an infinite variety of lattices with exact percolation thresholds to be generated we directly verify scullard s site percolation thresholds and derive the bond thresholds for his martini lattice p c 1 sqrt 2 and the a lattice p c 0 625457 dots solution to p 5 ensuremath 4 p 4 3 p 3 2 p 2 ensuremath 1 0 we also present a precise monte carlo test of the site threshold for the a lattice

non interleaving bisimulation equivalences on basic parallel processes we show polynomial time algorithms for deciding hereditary history preserving bisimilarity in o n 3logn and history preserving bisimilarity in o n 6 on the class basic parallel processes the latter algorithm also decides a number of other non interleaving behavioural equivalences e g distributed bisimilarity which are known to coincide with history preserving bisimilarity on this class the common general scheme of both algorithms is based on a fixpoint characterization of the equivalences for tree like labelled event structures the technique for realizing the greatest fixpoint computation in the case of hereditary history preserving bisimilarity is based on the revealed tight relationship between equivalent tree like labelled event structures in the case of history preserving bisimilarity a technique of deciding classical bisimilarity on acyclic petri nets is used

decidability of performance equivalence for basic parallel processes we study an extension of the class of basic parallel processes bpp in which actions are durational and urgent and parallel components have independent local clocks the main result is decidability of strong bisimilarity known also as performance equivalence in this class this extends the earlier decidability result for plain bpp by christensen et al our decision procedure is based on decidability of the validity problem for presburger arithmetic we prove also polynomial complexity in positive duration fragment thus properly extending a previous result by berard et al both ill timed and well timed semantics are treated

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

exact site percolation thresholds using a site to bond transformation and the star triangle transformation i construct a two dimensional lattice on which the inhomogeneous site percolation threshold is exactly calculable and use this result to find two more lattices on which the site thresholds can be determined the primary lattice studied here the martini lattice is a hexagonal lattice with every second site transformed into a triangle the site threshold of this lattice is found to be 0 764826 i e the solution to p4 3p3 1 0 while the others have square root 5 1 2 the inverse of the golden ratio and 1 square root 2 this last solution suggests a possible approach to establishing the bound for the hexagonal site threshold pc 1 square root 2 to derive these results i solve a correlated bond problem on the hexagonal lattice by use of the star triangle transformation and then by a particular choice of correlations derived from a site to bond transformation solve the site problem on the martini lattice

absolute versus relative time in process algebras abstract timed process algebras are useful tools for the specification and verification of real time systems we study the relationships between two of these algebras c i pa closed interval process algebra and tccs temporal ccs which deal with temporal aspects of concurrent systems by following very different interpretations durational actions versus durationless actions absolute time versus relative time timed functional behavior versus time and functional behavior local clocks versus global clocks we show that these different choices are not irreconcilable by presenting simple mappings from c i pa to tccs which preserve the behavioral equivalences over the two timed calculi these results hold whenever basic actions are interpreted as either eager or lazy whenever the starting time of action execution is observed rather than their completion time a study on the size of the labelled transition systems describing the transitional semantics of cipa processes and those describing the transitional semantics of their translated versions is also presented

parallel tempering cluster algorithm for computer simulations of critical phenomena in finite size scaling analyses of monte carlo simulations of second order phase transitions one often needs an extended temperature range around the critical point by combining the parallel tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest we introduce a flexible and powerful method for systematic investigations of critical phenomena as a result we gain one to two orders of magnitude in the performance for two and three dimensional ising models in comparison with the recently proposed wang landau recursion for cluster algorithms based on the multibondic algorithm which is already a great improvement over the standard multicanonical variant

tight bounds for the bond percolation threshold of the 3 122 lattice improved mathematically rigorous upper and lower bounds for the bond percolation threshold are established using the substitution method the lower bound is greater than 0 739 830 which was conjectured by tsallis to be the exact value of the percolation threshold together the bounds determine the first three digits of the threshold the results are obtained using computational improvements to the substitution method in which stochastic ordering is checked using a network flow algorithm

some exact results on bond percolation we present some exact results on bond percolation we derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice by l bonds connecting the same adjacent vertices thereby yielding the lattice l this relation is used to calculate the bond percolation threshold on l we show that this bond inflation leaves the universality class of the percolation transition invariant on a lattice of dimensionality d 2 but changes it on a one dimensional lattice and quasi one dimensional infinite length strips we also present analytic expressions for the average cluster number per vertex and correlation length for the bond percolation problem on the n limits of several families of n vertex graphs finally we explore the effect of bond vacancies on families of graphs with the property of bounded diameter as n

exact solution for the extended debye theory of dielectric relaxation of nematic liquid crystals abstract the exact solution for the transverse i e in the direction perpendicular to the director axis component of a nematic liquid crystal and the corresponding correlation time t is presented for the uniaxial potential of martin et al symp faraday soc 5 1971 119 the corresponding longitudinal i e parallel to the director axis quantities t may be determined by simply replacing magnetic quantities by the corresponding electric ones in our previous study of the magnetic relaxation of single domain ferromagnetic particles coffey et al phys rev e 49 1994 1869 the calculation of is accomplished by expanding the spatial part of the distribution function of permanent dipole moment orientations on the unit sphere in the fokker planck equation in normalised spherical harmonics this leads to a three term recurrence relation for the laplace transform of the transverse decay functions the recurrence relation is solved exactly in terms of continued fractions the zero frequency limit of the solution yields an analytic formula for the transverse correlation time t which is easily tabulated for all nematic potential barrier heights a simple analytic expression for t which consists of the well known meier saupe formula mol cryst 1 1966 515 with a substantial correction term which yields a close approximation to the exact solution for all and the correct asymptotic behaviour is also given the effective eigenvalue method is shown to yield a simple formula for t which is valid for all it appears that the low frequency relaxation process for both orientations of the applied field is accurately described in each case by a single debye type mechanism with corresponding relaxation times t t

undecidability of performance equivalence of petri nets abstract we investigate bisimulation equivalence on petri nets under durational semantics our motivation was to verify the conjecture that in durational setting the bisimulation equivalence checking problem becomes more tractable than in ordinary setting which is the case e g over communication free nets we disprove this conjecture in three of four proposed variants of durational semantics the fourth variant remains an intriguing open problem

microcanonical monte carlo study of a two dimensional blume capel model a microcanonical monte carlo algorithm has been developed to calculate the density of states of a two dimensional blume capel model in zero field the full density of states is calculated for a 16 16 lattice as a function of the two spin summations which appear in the hamiltonian this permits the partition function and related thermodynamic functions to be evaluated for any temperature and any single site anisotropy from a single data set results are presented for the pseudo critical transition temperature and the maximum in the specific heat as a function of the single site anisotropy parameter the technique will allow the region near the tricritical point to be explored in detail and will permit the future determination of the zeros of the partition function it should be noted that the microcanonical sampling method of lee 1990 was found to be unusably slow for the s 1 problem in regions were the density of states had a significant slope and the microcanonical sampling described in this work is a significant improvement on his sampling method

self consistent scaling theory for logarithmic correction exponents multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics here a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific heat critical exponent vanishes also the theory is widened to encompass the correlation function the new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made

exact bond percolation thresholds in two dimensions recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices here we show how these results can be extended to other classes of graphs significantly increasing the number and variety of solved problems any graph that can be decomposed into a certain arrangement of triangles which we call self dual gives a class of lattices whose percolation thresholds can be found exactly by a recently introduced triangle triangle transformation we use this method to generalize wierman s solution of the bow tie lattice to yield several new solutions we also give another example of a self dual arrangement of triangles that leads to a further class of solvable problems there are certainly many more such classes

a process algebra for timed systems a standard process algebra is extended by a new action which is meant to denote idling until the next clock cycle a semantic theory based on testing is developed for the new language this is characterised in terms of barbs a variety of ready traces and also characterised as the initial theory generated by a set of equations

strong violation of critical phenomena universality wang landau study of the two dimensional blume capel model under bond randomness we study the pure and random bond versions of the square lattice ferromagnetic blume capel model in both the first order and second order phase transition regimes of the pure model phase transition temperatures thermal and magnetic critical exponents are determined for lattice sizes in the range l 20 100 via a sophisticated two stage numerical strategy of entropic sampling in dominant energy subspaces using mainly the wang landau algorithm the second order phase transition emerging under random bonds from the second order regime of the pure model has the same values of critical exponents as the two dimensional ising universality class with the effect of the bond disorder on the specific heat being well described by double logarithmic corrections our findings thus supporting the marginal irrelevance of quenched bond randomness on the other hand the second order transition emerging under bond randomness from the first order regime of the pure model has a distinctive universality class with nu 1 30 6 and beta nu 0 128 5 these results amount to a strong violation of universality principle of critical phenomena since these two second order transitions with different sets of critical exponents are between the same ferromagnetic and paramagnetic phases furthermore the latter of these two sets of results supports an extensive but weak universality since it has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional systems with and without quenched disorder in the conversion by bond randomness of the first order transition of the pure system to second order we detect by introducing and evaluating connectivity spin densities a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness

universal ratio of magnetization moments in two dimensional ising models the authors calculate the universal critical point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic ising models on the square and on the triangular lattices periodic boundary conditions are used in accordance with the four fold and six fold rotational symmetries of the respective lattices these results which are obtained by means of an analysis of finite size data computed with a transfer matrix technique have an accuracy of the order of one millionth this analysis is also applied to rectangular systems with arbitrary aspect ratios

escape times for rigid brownian rotators in a bistable potential from the time evolution of the green function and the characteristic time of the probability evolution abstract the greatest relaxation time for an assembly of three dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions averages of the legendre polynomials of the system this is accomplished by studying the entire time evolution of the green function transition probability by expanding the time dependent distribution as a fourier series and proceeding to the zero frequency limit of the laplace transform of that distribution the procedure is entirely analogous to the calculation of the characteristic time of the probability evolution the integral of the configuration space probability density function with respect to the position co ordinate for a particle undergoing translational diffusion in a potential a concept originally used by malakhov and pankratov physica a 229 1996 109 this procedure allowed them to obtain exact solutions of the kramers one dimensional translational escape rate problem for piecewise parabolic potentials the solution was accomplished by posing the problem in terms of the appropriate sturm liouville equation which could be solved in terms of the parabolic cylinder functions the method as applied to rotational problems and posed in terms of recurrence relations for the decay functions i e the brinkman approach c f blomberg physica a 86 1977 49 as opposed to the sturm liouville one demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function albeit coupled to all the others in non linear fashion via the underlying recurrence relation is governed by a sum of decay functions the method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non axially symmetric potentials where the distribution function is governed by two state variables

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

multicritical points and crossover mediating the strong violation of universality wang landau determinations in the random bond d 2 blume capel model the effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic blume capel model are discussed the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method for many values of the crystal field restricted here in the second order phase transition regime of the pure model for the random bond version several disorder strengths are considered we present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex first order regime the critical properties of the pure model are contrasted and compared to those of the random model accepting for the weak random version the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random bond models the behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed it is pointed out that this complexity is related to the ground state structure of the random bond version

rigorous confidence intervals for critical probabilities we use the method of balister bollobas and walters random struct algorithms 26 392 2005 to give rigorous 99 9999 confidence intervals for the critical probabilities for site and bond percolation on the 11 archimedean lattices in our computer calculations the emphasis is on simplicity and ease of verification rather than obtaining the best possible results nevertheless we obtain intervals of width at most 0 0005 in all cases

on the semantics of durational actions this paper develops a mathematical framework to describe and reason about semantic theories of processes where actions have a non zero duration the framework relies on the notions of reduction and observability and allows one to naturally explain the possible choices to incorporate timing information in terms of process interaction mechanisms the framework provides a parameterized context where well known and new theories can be formally compared and classified by a suitable instantiation of the parameters a proof technique to derive from the reduction semantics an equivalent sos based characterization is also provided

transfer matrix computation of generalized critical polynomials in percolation percolation thresholds have recently been studied by means of a graph polynomial pb p henceforth referred to as the critical polynomial that may be defined on any periodic lattice the polynomial depends on a finite subgraph b called the basis and the way in which the basis is tiled to form the lattice the unique root of pb p in 0 1 either gives the exact percolation threshold for the lattice or provides an approximation that becomes more accurate with appropriately increasing size of b initially pb p was defined by a contraction deletion identity similar to that satisfied by the tutte polynomial here we give an alternative probabilistic definition of pb p which allows for much more efficient computations by using the transfer matrix than was previously possible with contraction deletion we present bond percolation polynomials for the 4 82 kagome and 3 122 lattices for bases of up to respectively 96 162 and 243 edges much larger than the previous limit of 36 edges using contraction deletion we discuss in detail the role of the symmetries and the embedding of b for the largest bases we obtain the thresholds pc 4 82 0 676 803 329 pc kagome 0 524 404 998 pc 3 122 0 740 420 798 comparable to the best simulation results we also show that the alternative definition of pb p can be applied to study site percolation problems this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

percolation thresholds on two dimensional voronoi networks and delaunay triangulations the site percolation threshold for the random voronoi network is determined numerically with the result pc 0 714 10 0 000 02 using monte carlo simulation on periodic systems of up to 40 000 sites the result is very close to the recent theoretical estimate pc approximately 0 7151 of neher for the bond threshold on the voronoi network we find pc 0 666 931 0 000 005 implying that for its dual the delaunay triangulation pc 0 333 069 0 000 005 these results rule out the conjecture by hsu and huang that the bond thresholds are 2 3 and 1 3 respectively but support the conjecture of wierman that for fully triangulated lattices other than the regular triangular lattice the bond threshold is less than 2 sin pi 18 approximately 0 3473

site percolation on planar phi 3 random graphs in this paper site percolation on random phi 3 planar graphs is studied by monte carlo numerical techniques the method consists in randomly removing a fraction q 1 p of vertices from graphs generated by monte carlo simulations where p is the occupation probability the resulting graphs are made of clusters of occupied sites by measuring several properties of their distribution it is shown that percolation occurs for an occupation probability above a percolation threshold p c 0 7360 5 moreover critical exponents are compatible with those analytically known for bond percolation

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

universality of the ising and the s 1 model on archimedean lattices a monte carlo determination the ising models s 1 2 and s 1 are studied by efficient monte carlo schemes on the 3 4 6 4 and the 3 3 3 3 6 archimedean lattices the algorithms used a hybrid metropolis wolff algorithm and a parallel tempering protocol are briefly described and compared with the simple metropolis algorithm accurate monte carlo data are produced at the exact critical temperatures of the ising model for these lattices their finite size analysis provide with high accuracy all critical exponents which as expected are the same with the well known 2d ising model exact values a detailed finite size scaling analysis of our monte carlo data for the s 1 model on the same lattices provides very clear evidence that this model obeys also very well the 2d ising model critical exponents as a result we find that recent monte carlo simulations and attempts to define effective dimensionality for the s 1 model on these lattices are misleading accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two archimedean lattices

estimation of bond percolation thresholds on the archimedean lattices we give accurate estimates for the bond percolation critical probabilities on seven archimedean lattices for which the critical probabilities are unknown using an algorithm of newman and ziff

determination of the bond percolation threshold for the kagome lattice the hull gradient method is used to determine the critical threshold for bond percolation on the two dimensional kagome lattice and its dual the dice lattice for this system the hull walk is represented as a self avoiding trail or mirror model trajectory on the 3 4 6 4 archimedean tiling lattice the result one standard deviation of error is not consistent with previously conjectured values

on bond percolation threshold bounds for archimedean lattices with degree three improved bounds are proved for bond percolation thresholds for certain archimedean lattices using the substitution method with new comparisons between models and more efficient computational techniques results obtained are and these bounds provide positive bounds on the difference between the site and bond percolation thresholds of these lattices and prove that the bond percolation thresholds of the and lattices are both strictly greater than that of the hexagonal lattice in the process of obtaining these results bounds for the kagome lattice bond percolation threshold were improved to

probability distribution function for reorientations in maier saupe potential abstract exact analytic solution for the probability distribution function of the non inertial rotational diffusion equation i e of the smoluchowski one in a symmetric maier saupe uniaxial potential of mean torque is obtained via the confluent heun s function both the ordinary maier saupe potential and the double well one with variable barrier width are considered thus the present article substantially extends the scope of the potentials amenable to the treatment by reducing smoluchowski equation to the confluent heun s one the solution is uniformly valid for any barrier height we use it for the calculation of the mean first passage time also the higher eigenvalues for the relaxation decay modes in the case of ordinary maier saupe potential are calculated the results obtained are in full agreement with those of the approach developed by coffey kalmykov dejardin and their coauthors in the whole range of barrier heights

exact curie temperature for the ising model on archimedean and laves lattices using the feynman vdovichenko combinatorial approach to the two dimensional ising model we determine the exact curie temperature for all two dimensional archimedean lattices by means of duality we extend our results to cover all two dimensional laves lattices for those lattices where the exact critical temperatures are not yet exactly known we compare them with monte carlo simulations