demixing can occur in binary hard sphere mixtures with negative nonadditivity a binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma sigma 2 sigma 1 infinity a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2 d is found even for slightly negative nonadditivity if delta 1 8 ln gamma 2 arguments concerning the stability of the demixing with respect to freezing are provided

generalized geometric cluster algorithm for fluid simulation we present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids the connection with well known cluster algorithms for lattice spin models is discussed and an explicit full cluster decomposition is derived for a particle configuration in a fluid we investigate a number of basic properties of the geometric cluster algorithm including the dependence of the cluster size distribution on density and temperature practical aspects of its implementation and possible extensions are discussed the capabilities and efficiency of our approach are illustrated by means of two example studies

anomalous multifractality of conductance jumps in a hierarchical percolation model the authors have investigated the multifractal scaling of conductance jumps in a hierarchical percolation lattice resulting from cutting the current carrying bonds in the lattice due to the iterative nature of the model exact renormalization group rg equations are obtained and used to extract the minimum conductance jump of the lattice they find an asymptotically analytic expression for the minimum conductance jump delta gmin approximately exp c log l 2 decreasing faster than any power law they observed slow convergence to the asymptotic behaviour due to the importance of the irrelevant terms in the rg equations at low generations of the lattice numerical calculations are performed in order to validate the analytic results and to calculate the f alpha spectrum to confirm left sided multifractality as proposed by lee and stanley 1988

anomalous crossover behaviours in the two component deterministic percolation model the authors have investigated the current distribution in the two component deterministic percolation model in which the ratio h of poor to good conductance is regarded as a small parameter it is found that the minimum current imin h scales anomalously with h imin h imin 1 exp constant ln h 2 h hlphi where l is the size of the network h a function describing the crossover from fractal to homogeneous behaviours and phi the crossover exponent the exponential prefactor is quite similar to the behaviour of left sided multifractality in diffusion limited aggregations it is found that phi coincides with the crossover exponent for all multifractal moments of the current distribution

binary nonadditive hard sphere mixtures at high dimension at high spatial dimension a suitably scaled classical system of interacting particles truncates at second virial terms a binary mixture of nonadditive hard spheres with sufficiently repulsive interaction between unlike particles decomposes at sufficiently high density into two coexisting phases the region around the critical density behaves classically

composition factors of tensor products of truncated symmetric powers let g be the general linear group of degree n over an algebraically closed field k of characteristic p 0 we study the m fold tensor product s e m of the truncated symmetric algebra s e of the symmetric algebra s e of the natural module e for g we are particularly interested in the set of partitions occurring as the highest weight of a composition factor of s e m we explain how the determination of these composition factors is related to the determination of the set of composition factors of the m fold tensor product s e m of the symmetric algebra we give a complete description of the composition factors of s e m in terms of distinguished partitions our main interest is in the classical case but since the quantised version is essentially no more difficult we express our results in the general context throughout

direct correlation functions of the widom rowlinson model abstract we calculate through monte carlo mc numerical simulations the partial total and direct correlation functions of the three dimensional symmetric widom rowlinson mixture we find that the differences between the partial direct correlation functions from simulation and from the percus yevick approximation calculated analytically by ahn and lebowitz are well fitted by gaussians we provide an analytical expression for the fit parameters as function of the density we also present mc simulation data for the direct correlation functions of a couple of non additive hard sphere systems to discuss the modification induced by finite like diameters

metabelian lie powers of the natural module for a general linear group abstract consider a free metabelian lie algebra m of finite rank r over an infinite field k of prime characteristic p given a free generating set m acquires a grading its group of graded automorphisms is the general linear group g l r k so each homogeneous component m d is a finite dimensional g l r k module the homogeneous component m 1 of degree 1 is the natural module and the other m d are the metabelian lie powers of the title this paper investigates the submodule structure of the m d in the main result a composition series is constructed in each m d and the isomorphism types of the composition factors are identified both in terms of highest weights and in terms of steinberg s twisted tensor product theorem their dimensions are also given it turns out that the composition factors are pairwise non isomorphic from which it follows that the submodule lattice is finite and distributive by the birkhoff representation theorem any such lattice is explicitly recognizable from the poset of its join irreducible elements the poset relevant for m d is then determined by exploiting a 1975 paper of yu a bakhturin on identical relations in metabelian lie algebras

phase diagram of highly asymmetric binary hard sphere mixtures we study the phase behavior and structure of highly asymmetric binary hard sphere mixtures by first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective hamiltonian of the large spheres then using an explicit pairwise depletion potential approximation to this effective hamiltonian in computer simulations we determine fluid solid coexistence for size ratios q 0 033 0 05 0 1 0 2 and 1 0 the resulting two phase region becomes very broad in packing fractions of the large spheres as q becomes very small we find a stable isostructural solid solid transition for ql 0 05 and a fluid fluid transition for ql 0 10 however the latter remains metastable with respect to the fluid solid transition for all size ratios we investigate in the limit stackrel ensuremath rightarrow q 0 the phase diagram mimics that of the sticky sphere system as expected the radial distribution function g r and the structure factor s k of the effective one component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid solid boundary the value of s k at its first peak is much lower than the value given by the hansen verlet freezing criterion direct simulations of the true binary mixture of hard spheres were performed for qg 0 05 in order to test the predictions from the effective hamiltonian for those packing fractions of the small spheres where direct simulations are possible we find remarkably good agreement between the phase boundaries calculated from the two approaches even up to the symmetric limit q 1 and for very high packings of the large spheres where the solid solid transition occurs in both limits one might expect that an approximation which neglects higher body terms should fail but our results support the notion that the main features of the phase equilibria of asymmetric binary hard sphere mixtures are accounted for by the effective pairwise depletion potential description we also compare our results with those of other theoretical treatments and experiments on colloidal hard sphere mixtures

hall effect on multifractality of current distribution of percolation threshold the author investigates the scaling behaviour of the current distribution in the random resistor network at the percolation threshold under a weak magnetic field a self dual fractal model is used to mimic the two dimensional percolation cluster at the threshold the infinite set of exponents is calculated for the moments of the ohmic and hall current distribution on the regular fractal the dependence of the multifractality on the magnetic field by the hall effect is shown it is found that the ohmic and hall current distribution shows a characteristic multifractality under a magnetic field

freezing transition of hard hyperspheres we investigate the system of d dimensional hard spheres in d dimensional space where d 3 for the fluid phase of these hyperspheres we generalize scaled particle theory to arbitrary d and furthermore use the virial expansion and the percus yevick integral equation for the crystalline phase we adopt cell theory based on elementary geometrical assumptions about close packed lattices regardless of the approximation applied and for dimensions as high as d550 we find a first order freezing transition which preempts the kirkwood second order instability of the fluid the relative density jump increases with d and a generalized lindemann rule of melting holds we have also used ideas from fundamental measure theory to obtain a free energy density functional for hard hyperspheres finally we have calculated the surface tension of a hypersphere fluid near a hard smooth hyper wall within scaled particle theory

exact solution of the percus yevick equation for a hard core fluid in odd dimensions it is shown that the percus yevick integral equation for the pair distribution function of a fluid interacting with a hard core potential can be solved not only in one and three dimensions where the solution is well known but more generally in all odd dimensions the nonlinear integral equation is reduced to an algebraic equation of order d 3 for odd dimensions d greater than three as an example the direct correlation function in five dimensions is derived explicitly

spontaneous magnetization in the plane the arak process is a solvable stochastic process which generates coloured patterns in the plane patterns are made up of a variable number of random non intersecting polygons we show that the distribution of arak process states is the gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble the sequence of gibbs distributions forms a new model parameterised by temperature we prove that there is a phase transition in this model for some non zero temperature we illustrate this conclusion with simulation results we measure the critical exponents of this off lattice model and find they are consistent with those of the ising model in two dimensions

structure of hard hypersphere fluids in odd dimensions the structural properties of single component fluids of hard hyperspheres in odd space dimensionalities d are studied with an analytical approximation method that generalizes the rational function approximation earlier introduced in the study of hard sphere fluids s b yuste and a santos phys rev a 43 5418 1991 the theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in laplace space the coefficients being determined by simple physical requirements fourier transform in terms of reverse bessel polynomials constitute the mathematical framework of this approximation from which an analytical expression for the static structure factor is obtained in its most elementary form the method recovers the solution of the percus yevick closure to the ornstein zernike equation for hyperspheres at odd dimensions the present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state excellent agreement with available computer simulation data at d 5 and d 7 is obtained

a free energy bound for the hopfield model the author gives a simple upper and lower bound on the free energy density of the hopfield model of size n with p stored patterns in the limit where n and p tend to infinity with p n to alpha 1 the two bounds coincide for alpha 0

anomalous crossover behaviors in the two component random resistor network abstract it has been found from numerical simulation that the minimum current in the two component random resistor network at percolation scales anomalously with the ratio h of poor to good conductances i min h exp constant ln h 2 exact analytic calculations in the hierarchical diamond lattice confirm the result the exponential prefactor is analogous to the behavior of left sided multifractality in diffusion limited aggregations

theory of asymmetric nonadditive binary hard sphere mixtures it is shown that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard sphere mixture works equally well for nonadditive as it does for additive mixtures for highly asymmetric mixtures small size ratios the resulting effective hamiltonian of the one component fluid of big spheres which consists of an infinite number of many body interactions should be accurately approximated by truncating after the term describing the effective pair interaction using a density functional treatment developed originally for additive hard sphere mixtures the zero one and two body contribution to the effective hamiltonian are determined it is demonstrated that even small degrees of positive or negative nonadditivity have significant effect on the shape of the depletion potential the second virial coefficient b2 corresponding to the effective pair interaction between two big spheres is found to be a sensitive measure of the effects of nonadditivity the variation of b2 with the density of the small spheres shows significantly different behavior for additive slightly positive and slightly negative nonadditive mixtures possible repercussions of these results for the phase behavior of binary hard sphere mixtures are discussed and it is suggested that measurements of b2 might provide a means of determining the degree of nonadditivity in real colloidal mixtures

current distribution and local power dissipation in the two component deterministic percolation model the authors have investigated the current distribution and local power dissipation in the two component deterministic percolation model in which the ratio of conductance h is regarded as a small parameter the iterative nature of the model enables them to find exact recursion relations for the current distribution for an extremely small h such that hlphi 1 where l is the size of the lattice and phi the crossover exponent they find that d alpha approximately exp a alpha b log l 2 log l 3 where d alpha d alpha is the number of currents with alpha log ii alpha d alpha ii is the current in bond i and a b are constants the current distribution is well approximated by a gaussian with the mean varying with the size as log l 2 while the variance as log l 3 as a result both the most probable current and the minimum current scale with l as exp constant log l 2 similar results are obtained for the distribution of local power dissipation

mean field theory of the potts gas we consider a gas of classical particles in r d having q distinct colours interacting via a mean field potts potential and subject to an external field a colour independent molecular interaction of mean field type is also admitted in contrast to the usual lattice potts model the potts gas exhibits the specific volume v as a parameter in addition to colour ordering the v dependence of the potts gas is studied in detail and the complete phase diagram is derived it turns out that for q 3 the transition to colour ordering implies a jump of density for q 2 this transition is continuous but may become discontinuous under the influence of a suitable molecular interaction

monte carlo study of the widom rowlinson fluid using cluster methods the widom rowlinson model of a fluid mixture is studied using a new cluster algorithm that is an adaptation of the invaded cluster method previously applied to potts models the algorithm overcomes the difficulties of treating continuum hard core systems and has almost no critical slowing down our estimates of byn and gyn for the two component fluid are consistent with the ising universality class in two and three dimensions we also present preliminary results for the three component fluid s0031 9007 97 04175 6 pacs numbers 05 50 q 64 60 fr 75 10 hk some years ago widom and rowlinson 1 introduced a simple continuum model that exhibits a phase transition 2 the two component version of this model consists of black and white particles particles of the same type do not interact but particles of differing type experience a hard core repulsion at separations less than or equal to s 3 we present a new monte carlo method for simulating the widom rowlinson wr model and apply the method to study the demixing transition in two and three dimensions there have been few monte carlo studies of the wr critical point because of the difficulties of treating hardcore systems and critical slowing down using standard monte carlo techniques we discuss a new algorithm that overcomes these difficulties using cluster methods of the type introduced by swendsen and wang 4 the algorithm employs the invaded cluster ic approach 5 6 to locate the critical point we find that the algorithm has almost no critical slowing down and that we can obtain accurate values of the critical density and the exponent ratios byn and gyn with modest computational effort the two component wr model is expected to be in the ising universality class our results for byn and gyn are consistent with this assumption and our value for the critical density of the three dimensional d 3 w r model agrees with recent results obtained in ref 7 we also consider a wr model in which there are q components any two of which interact via a hard core repulsion 8 9 our algorithm easily extends to these q component wr models and we present results for the three component model in d 2 3 graphical representations of the wr model a configuration of the wr fluid consists of two sets of points s and t corresponding to the positions of the black and white particles in the grand canonical ensemble the probability density for finding the configuration ss td is

a new singular behaviour in current distribution of random resistor networks the authors study the singular behaviour occurring in delta alpha q delta q of the multifractal spectrum for the current distribution in random resistor networks the singular behaviour may be understood as the divergent behaviour of specific heat in a thermodynamic phase transition delta alpha q delta q shows a peak with the width q0 l q qc l and the height of which diverges as the system size l increases however the nature of the singular behaviour in delta alpha q delta q is very unusual compared with that of the ordinary phase transition in the following ways first the width of the peak becomes broader rather than narrower with the increasing system size l because q0 l to infinity and qc l to 0 as l to infinity second the singularities at q q0 and q qc are of different types the singularity at q q0 is of power law type such as approximately ld 2 m m log l and the singularity at q qc is of logarithmic type such as approximately log l 2m where d is spatial dimension and m is measured to be approximately 1 633 or 0 006

graphical representations and cluster algorithms ii we continue the study initiated in part i of graphical representations and cluster algorithms for various models in or related to statistical mechanics for certain models e g the blume emery griffths model and various generalizations we develop fortuin kasteleyn type representations which lead immediately to swendsen wang type algorithms for other models e g the random cluster model that are defined by a graphical representation we develop cluster algorithms without reference to an underlying spin system in all cases phase transitions are related to percolation or incipient percolation in the graphical representation which via the ic algorithm allows for the rapid simulation of these systems at the transition point pertinent examples include the continuum widom rowlinson model the restricted 1 step solid on solid model and the xy model

a note on the adjoint action of a semisimple group on the coordinate algebra of an infinitesimal subgroup abstract let g be a connected semisimple simply connected algebraic group over an algebraically closed field k of positive characteristic the action of g on itself by conjugation induces on the coordinate algebra k g and hence on the coordinate algebra k g r of the infinitesimal subgroup g r the structure of a rational g module in the recent paper 3 by bendel nakano pillen and sobaje the authors ask whether the tensor product of k g r with the rth steinberg module st r has a good filtration here we show that this is the case provided that the characteristic of k is good for g we do so by relating k g r to a certain quotient of the coordinate algebra k g of the lie algebra g of g and using a koszul resolution we note that the argument may also be applied to certain polynomial modules occurring in the context of doty s conjecture 17 4 2 11

toy model for the mean field theory of hard sphere liquids we investigate a toy model of liquid based on simplified hypernetted chain equations in very large spatial dimension d the model does not exhibit a phase transition but several regimes of behavior when d infinity can be observed in different intervals of the density

an integral equation theory for the widom rowlinson mixture the widom rowlinson mixture is a two component fluid in which like species do not interact and unlike species interact via a hard core repulsion as the density is increased this fluid phase separates standard integral equation approaches such as the percus yevick or hypernetted chain or thermodynamically self consistent hybirds of these two make very inaccurate predictions for the location of this critical point in the three dimensional model in this article we suggest a family of new approximations for this model that rely on incorporating terms in the density expansion of the direct correlation function into the closure approximation we show that the simplest of these closures is significantly more accurate than previous theories for the structure and thermodynamics of the fluid