limitations on universality in the continuous spin ising model the authors give by explicit counterexample numerical evidence that critical exponent universality fails for the two dimensional continuous spin ising model this result is contrary to what has previously been assumed

universal configurational structure in two dimensional scalar models monte carlo methods are used to explore the universal configurational structure of two dimensional spin 1 2 spin 1 and border phi 4 models comparison of spin 1 2 and spin 1 data provides evidence that the magnetisation distribution effectively the helmholtz free energy function and its coupling derivative effectively the internal energy function constitute readily accessible signatures of a universality class it is shown that when allowance is made for relatively large corrections to scaling effects the behaviour of the border phi 4 model may be satisfactorily matched to that of the other two models substantiating the view that the border model does indeed belong to the ising universality class

fast summation at nonequispaced knots by nfft we develop a new algorithm for the fast computation of discrete sums f y j sum k 1 n alpha k k y j x k j 1 m based on the recently developed fast fourier transform fft at nonequispaced knots our algorithm in particular our regularization procedure is simply structured and can be easily adapted to different kernels k our method utilizes the widely known fft and can consequently incorporate advanced fft implementations in summary it requires cal o n log n m arithmetic operations we prove error estimates to obtain clues about the choice of the involved parameters and present numerical examples in one and two dimensions

critical phenomena at surfaces in a model of nonequilibrium phase transitions critical phenomena at surfaces are studied in a simple two dimensional model of non equilibrium phase transitions belonging to the class of interacting particle systems the mean field renormalization group approach and numerical simulations are used to determine the phase diagram for this system and some of the critical exponents associated with ordinary special extraordinary and surface phase transitions

direct inversion of the nonequispaced fast fourier transform abstract various applications such as mri solution of pdes etc need to perform an inverse nonequispaced fast fourier transform nfft i e compute m fourier coefficients from given n nonequispaced data in the present paper we consider direct methods for the inversion of the nfft we introduce algorithms for the setting m n as well as for the underdetermined and overdetermined cases for the setting m n a direct method of complexity o n log n is presented which utilizes lagrange interpolation and the fast summation for the remaining cases we use the matrix representation of the nfft to deduce our algorithms thereby we are able to compute an inverse nfft up to a certain accuracy by means of a modified adjoint nfft in o m log m n arithmetic operations finally we show that these approaches can also be explained by means of frame approximation

analysis of earlier times and flux of entropy on the majority voter model with diffusion we study the properties of nonequilibrium systems modelled as spin models without defined hamiltonian as the majority voter model this model has transition probabilities that do not satisfy the condition of detailed balance the lack of detailed balance leads to entropy production phenomena which are a hallmark of the irreversibility by considering that voters can diffuse on the lattice we analyze how the entropy production and how the critical properties are affected by this diffusion we also explore two important aspects of the diffusion effects on the majority voter model by studying entropy production and entropy flux via time dependent and steady state simulations this study is completed by calculating some critical exponents as function of the diffusion probability

universal features and tail analysis of the order parameter distribution of the two dimensional ising model an entropic sampling monte carlo study we present a numerical study of the order parameter probability density function pdf of the square ising model for lattices with linear sizes l 80 140 a recent efficient entropic sampling scheme combining the wang landau and broad histogram methods and based on the high levels of the wang landau process in dominant energy subspaces is employed we find that for large lattices there exists a stable window of the scaled order parameter in which the full ansatz including the pre exponential factor for the tail regime of the universal pdf is well obeyed this window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal pdf the probability densities are used to estimate the universal privman fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime

monte carlo calculations of the conformal charge the conformal charge is an important quantity which characterizes the nature of the two dimensional phase transition we report a first attempt to use a new numerical method to calculate the conformal charge in this paper we apply our method to the 2 dimensional 4 continuous spin ising model by varying the parameters in the hamiltonian one can change continuously from the known gaussian limit to the ising limit it is well known that the critical points for these two systems are not in the same universality class we study this behavior for the gaussian model the single well 4 model the border model and the double well 4 model for a large lattice our results while giving a good general picture are not so far sufficient to differentiate whether the non gaussian cases studied belong to the ising model universality class or not further studies of other lattice sizes should serve to improve greatly our conclusions

phase ordering and persistence in a class of stochastic processes interpolating between the ising and voter models we study the dynamics of a class of two dimensional stochastic processes depending on two parameters which may be interpreted as two different temperatures respectively associated to interfacial and to bulk noise special lines in the plane of parameters correspond to the ising model voter model and majority vote model the dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing annihilating and branching random walkers we use the freedom allowed by the space of parameters to measure by numerical simulations the persistence probability of a generic model in the low temperature phase where the system coarsens this probability is found to decay at large times as a power law with a seemingly constant exponent we also discuss the connection between persistence and the nature of the interfaces between domains

finite size scaling analysis of the φ 4 field theory on the square lattice monte carlo calculations are performed for the model hamiltonian i r 2 2 i u 4 gf4 i c 2 i j 2 for various values of the parametersr u c in the crossover region from the ising limit r u to the displacive limit r 0 the variable i is a scalar continuous spin variable which can lie in the range i for each lattice site i i is a priori selected proportional to the single site probability in our monte carlo algorithm the critical line is obtained in very good agreement with other previous approaches a decrease of apparent critical exponents deduced from a finite size scaling analysis is attributed to a crossover toward mean field values at the displacive limit the relation of this model to the coarse grained landau ginzburg wilson free energy functional of ising models is discussed in detail and by matching local moments 2 i 4 i to corresponding averages of subsystem blocks of ising systems with linear dimensionsl 5 tol 15 an explicit construction of this coarse grained free energy is attempted self consistency checks applied to this matching procedure show qualitatively reasonable behavior but quantitative difficulties remain indicating that higher order terms are needed for a quantitatively satisfactory description

long range order for a kinetic ising model at infinite temperature abstract the two dimensional ising model in contact with a heat bath at infinite temperature t is considered the model is subject to two competing stochastic processes the glauber dynamics with probability p and the kawasaki one with probability 1 p the glauber process is associated to the random flipping of single spins at t while the spin exchange kawasaki dynamics occurs at t 0 what increases the energy of the system we show that the model exhibits a continuous transition from the paramagnetic to the antiferromagnetic phase at the critical value p c 0 073 0 003 we have used monte carlo simulations and finite size analysis in order to calculate the critical probability and the critical exponents of the model surprisingly our value found for the critical probability is almost the same as the critical noise parameter of the isotropic majority vote model on a square lattice

rapid computation of the discrete fourier transform algorithms for the rapid computation of the forward and inverse discrete fourier transform for points which are nonequispaced or whose number is unrestricted are presented the computational procedure is based on approximation using a local taylor series expansion and the fast fourier transform fft the forward transform for nonequispaced points is computed as the solution of a linear system involving the inverse fourier transform this latter system is solved using the iterative method gmres with preconditioning numerical results are given to confirm the efficiency of the algorithms

three state majority vote model on square lattice abstract here a non equilibrium model with two states 1 1 and a noise q on simple square lattices proposed for m j oliveira 1992 following the conjecture of up down symmetry of grinstein and colleagues 1985 is studied and generalized this model is well known today as the majority vote model they showed through monte carlo simulations that their obtained results fall into the universality class of the equilibrium ising model on a square lattice in this work we generalize the majority vote model for a version with three states now including the zero state 1 0 1 in two dimensions using monte carlo simulations we showed that our model falls into the universality class of the spin 1 1 0 1 and spin 1 2 ising model and also agree with majority vote model proposed for m j oliveira 1992 the exponent ratio obtained for our model was 1 77 3 0 121 5 and 1 1 03 5 the critical noise obtained and the fourth order cumulant were q c 0 106 5 and u 0 62 3

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

universal behavior in an irreversible model with c 3v symmetry we analyze the critical behavior of a two dimensional irreversible cellular automaton whose dynamic rules are invariant under the symmetry operations of the point group c 3v we study the dynamical phase transition that takes place in the model and obtain the static and short time critical exponents by the use of monte carlo simulations our results indicate that the present model is in the same universality class as the three state potts model

dynamical critical exponent for the majority vote model we investigate the dynamical behavior of the isotropic majority vote model on a square lattice using a combination of damage spreading and finite size scaling methods for initial damage d 0 1 2 the dynamical phase diagram exhibits a chaotic frozen phase transition at a critical noise parameter qc 0 0818 0 0002 while for d 0 1 2 the damage does not propagate for any value of the model s parameter 0 q 1 2 from simulations at qc we find that the dynamical critical exponent is z 0 65 0 05

critical behaviour of the non equilibrium ising model with locally competing temperatures the author uses a method which combines the ideas of the renormalisation group and mean field theory to obtain the phase diagram of two and three dimensional non equilibrium ising models with two locally competing temperatures comparison is made with available results of other authors an estimate of critical exponent nu is derived

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

isotropic majority vote model on a square lattice the stationary critical properties of the isotropic majority vote model on a square lattice are calculated by monte carlo simulations and finite size analysis the critical exponents and are found to be the same as those of the ising model and the critical noise parameter is found to beqc 0 075 0 001

a fast algorithm for chebyshev fourier and sinc interpolation onto an irregular grid a chebyshev or fourier series may be evaluated on the standard collocation grid by the fast fourier transform fft unfortunately the fft does not apply when one needs to sum a spectral series at n points which are spaced irregularly the cost becomes o n2 operations instead of the ffts o n log n this sort of off grid interpolation is needed by codes which dynamically readjust the grid every few time steps to resolve a shock wave or other narrow features it is even more crucial to semi lagrangian spectral algorithms for solving convection diffusion and navier stokes problems because off grid interpolation must be performed several times per time step in this work we describe an alternative algorithm the first step is to pad the set of spectral coefficients an with zeros and then take an fft of length 3n to interpolate the chebyshev series to a very fine grid the second step is to apply either the mth order euler sum acceleration or 2m 1 point lagrangian interpolation to approximate the sum of the series on the irregular grid we show that both methods yield full precision with m n allowing an order of magnitude reduction in cost with no loss of accuracy

opinion dynamics of random walking agents on a lattice the opinion dynamics of random walking agents on finite two dimensional lattices is studied in the model the opinion is continuous and both the lattice and the opinion can be either periodic or nonperiodic at each time step all agents move randomly on the lattice and update their opinions based on those of neighbors with whom the differences of opinion are not greater than a given threshold due to the effect of repeated averaging opinions first converge locally and eventually reach steady states as in other models with bounded confidence steady states in general are those with one or more opinion groups in which all agents have the same opinion when both the lattice and the opinion are periodic however metastable states can emerge in which the whole spectrum of location dependent opinions can coexist this result shows that when a set of continuous opinions forms a structure like a circle unlike the typically used linear opinions rich dynamic behavior can arise when there are geographical restrictions in real situations a complete consensus is rarely reached and metastable states here might be one of the explanations for these situations especially when opinions are not linear

time coarse graining near critical points the authors investigate the statistical properties of local variables coarse grained in time in systems undergoing continuous phase transitions a general theory is developed which suggests universal scaling behaviour in the limit of large coarse graining times the predictions are substantiated with monte carlo studies of two dimensional scalar models a simple fractal model of the time profile of the ordering variable is developed which captures and illuminates its timescale invariant character the theory is used to study the critical behaviour of local resonance lineshapes in the two dimensional case studied explicitly the critical slowing down is shown to drive a crossover to a split slow motion lineshape

phase transitions in the majority vote model with two types of noises abstract in this work we study the majority vote model with the presence of two distinct noises the first one is the usual noise q that represents the probability that a given agent follows the minority opinion of his her social contacts on the other hand we consider the independent behavior such that an agent can choose his her own opinion 1 or 1 with equal probability independent of the group s norm we study the impact of the presence of such two kinds of stochastic driving in the phase transitions of the model considering the mean field and the square lattice cases our results suggest that the model undergoes a nonequilibrium order disorder phase transition even in the absence of the noise q due to the independent behavior but this transition may be suppressed in addition for both topologies analyzed we verified that the transition is in the same universality class of the equilibrium ising model i e the critical exponents are not affected by the presence of the second noise associated with independence

existence of an upper critical dimension in the majority voter model we study the critical properties of the majority voter model on d dimensional hypercubic lattices in two dimensions the majority voter model belongs to the same universality class as that of the ising model however the critical behaviors of the majority voter model on four dimensions do not exhibit mean field behavior using the monte carlo simulation on d dimensional hypercubic lattices we obtain the critical exponents up to d 7 and find that the upper critical dimension is 6 for the majority voter model we also confirm our results using mean field calculation

damage spreading in the majority vote model on small world networks abstract we use the damage spreading technique to study the dynamical phase diagram and critical behavior of the isotropic majority vote model on small world networks generated by rewiring two dimensional square lattices the phase diagram exhibits a chaotic frozen phase transition at a critical noise parameter q c p which is a monotonically increasing function of the probability p of having long range interactions for the correlation length critical exponent we obtain the mean field value 1 2 for all systems with p 0 whereas the exponent ratio and the dynamical critical exponent z are both dependent on the fraction of shortcuts introduced in the system

finite size scaling for first order transitions potts model the finite size scaling algorithm based on bulk and surface renormalization of de oliveira is tesed onq state potts models in dimensionsd 2 and 3 our monte carlo data clearly distinguish between first and second order phase transitions continuous q analytic calculations performed for small lattices show a clear tendency of the magnetic exponenty d v to reach a plateau for increasing values ofq which is consistent with the first order transition valuey d monte carlo data confirm this trend

nonequilibrium spin models with ising universal behaviour the properties of a family of nonequilibrium spin models with up down symmetry on a square lattice are determined by a mean field pair approximation and by monte carlo simulation the phase diagram in the parameter space displays a critical line that terminates at a first order critical point it is found that the critical exponents are the same as those of the equilibrium ising model

majority vote model with different agents abstract we consider the majority vote model with noise in a network of social interactions for a system with two classes of individuals class and class for the two agent model each class has its own dynamics with individuals of class being influenced by neighbors of both classes while the individuals of type are influenced only by neighbors of that class we use monte carlo simulations and finite size scaling techniques to estimate the critical properties of the system in the stationary state the calculated values of the critical noise parameters q and q allow us to identify five distinct regions in the phase diagram on the q q plane the critical exponents for each class are the same and we conclude that the present model belongs to the same universality class as the two dimensional ising model

simulation of static critical phenomena in nonideal fluids with the lattice boltzmann method a fluctuating nonideal fluid at its critical point is simulated with the lattice boltzmann method it is demonstrated that the method employing a ginzburg landau free energy functional correctly reproduces the static critical behavior associated with the ising universality class a finite size scaling analysis is applied to determine the critical exponents related to the order parameter compressibility and specific heat a particular focus is put on finite size effects and issues related to the global conservation of the order parameter

a nonuniform fast fourier transform based on low rank approximation by viewing the nonuniform discrete fourier transform nudft as a perturbed version of a uniform discrete fourier transform we propose a fast and quasi optimal algorithm for computing the nudft based on the fast fourier transform fft our key observation is that an nudft and dft matrix divided entry by entry is often well approximated by a low rank matrix allowing us to express a nudft matrix as a sum of diagonally scaled dft matrices our algorithm is simple to implement automatically adapts to any working precision and is competitive with state of the art algorithms in the fully uniform case our algorithm is essentially the fft we also describe quasi optimal algorithms for the inverse nudft and two dimensional nudfts

a probabilistic automata network epidemic model with births and deaths exhibiting cyclic behaviour a probabilistic automata network model for the spread of an infectious disease in a population of moving individuals is studied the local rule consists of two subrules the first one applied synchronously models infection birth and death processes it is a probabilistic cellular automaton rule the second applied sequentially describes the motion of the individuals the model contains six parameters the probabilities p for a susceptible to become infected by contact with an infective the respective birth rates bs and bi of the susceptibles from either a susceptible or an infective parent the respective death rates ds and di of susceptibles and infectives and a parameter m characterizing the motion of the individuals the model has three fixed points the first is trivial it describes a stationary state with no living individuals the second corresponds to a disease free state with no infectives the third and last one characterizes an endemic state with non zero densities of susceptibles and infectives moreover the model may exhibit oscillatory behaviour of the susceptible and infective densities as functions of time through a hopf type bifurcation the influence of the different parameters on the stability of all these states is studied with a particular emphasis on the influence of motion which has been found to be a stabilizing factor of the cyclic behaviour

scaling properties of the cluster distribution of a critical nonequilibrium model abstract a geometric approach to critical fluctuations of a nonequilibrium model is reported the two dimensional majority vote model was investigated by monte carlo simulations on square lattices of various sizes and a detailed scaling analysis of cluster statistical and geometric properties was performed the cluster distribution exponents and fractal dimension were found to be the same as those of the two dimensional ising model this result which cannot be derived purely from the known bulk critical behaviour widens our knowledge about the range of validity of the ising universality class for nonequilibrium systems

local event boundary detection with unreliable sensors in this paper we study the identification of an event region x within a larger region y in which the sensors are distributed by a poisson process of density to detect this event region i e its boundary the model of sensor is a 0 1 sensor that decides whether it lies in x or not and which might be incorrect with probability p it also collects information on the 0 1 values of the neighbors within some distance r and revises its decision by the majority vote of these neighbors in the most general setting we analyze this simple majority vote scheme and derive some upper and lower bounds on the expected number of misclassified sensors these bounds depend on several sensing parameters of p r and some geometric parameters of the event region x by making some assumptions on the shape of x we prove a significantly improved upper bound on the expected number of misclassified sensors especially for convex regions with sufficiently round boundary and we find that the majority vote scheme performs better in the simulation rather than its theoretical upper bound

fast approximate fourier transforms for irregularly spaced data several algorithms for efficiently evaluating trigonometric polynomials at irregularly spaced points are presented and analyzed the algorithms can be viewed as approximate generalizations of the fast fourier transform fft and they are compared with regard to their accuracy and their computational efficiency

entropy production in the majority vote model we analyzed the entropy production in the majority vote model by using a mean field approximation and monte carlo simulations the dynamical rules of the model do not obey detailed balance so that entropy is continuously being produced this nonequilibrium stochastic model is known to have a critical behavior belonging to the universality class of the equilibrium ising model we show that the entropy production exhibits a singularity at the critical point whose exponent is estimated numerically

majority vote model with a bimodal distribution of noises in small world networks abstract we consider a generalized version of the majority vote model in small world networks in our model each site of the network has noise q 0 and q 0 with probability f and 1 f respectively the connections of the two dimensional square lattice are rewired with probability p we performed monte carlo simulations to characterize the order disorder phase transition of the system through finite size scaling analysis we calculated the critical noise value q c and the standard critical exponents 1 our results suggest that these exponents are different from those of the isotropic majority vote model we concluded that the zero noise fraction f when combined with the rewiring probability p drive the system to a different universality class from that of the isotropic majority vote model

ising model simulation in directed lattices and networks abstract on directed lattices with half as many neighbours as in the usual undirected lattices the ising model does not seem to show a spontaneous magnetisation at least for lower dimensions instead the decay time for flipping of the magnetisation follows an arrhenius law on the square and simple cubic lattice on directed barabasi albert networks with two and seven neighbours selected by each added site metropolis and glauber algorithms give similar results while for wolff cluster flipping the magnetisation decays exponentially with time

critical behavior of the majority voter model is independent of transition rates we study the critical properties of the majority voter model by using two different transition rates the glauber rate and the metropolis rate the model with the glauber rate has been found to be mapped to the majority voter model with noise de oliveira j stat phys 66 273 1992 the critical temperature and the critical exponents for the two transition rates are obtained from a monte carlo simulation with a finite size scaling analysis the critical temperature is found to depend on the transition rate but the critical exponents do not the values of the critical exponents obtained indicate that the model belongs to the same universality class as the ising model regardless of the type of transition rate

accelerating the nonuniform fast fourier transform the nonequispaced fourier transform arises in a variety of application areas from medical imaging to radio astronomy to the numerical solution of partial differential equations in a typical problem one is given an irregular sampling of n data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain when the sampling is uniform the fast fourier transform fft allows this calculation to be computed in o n log n operations rather than o n 2 operations unfortunately when the sampling is nonuniform the fft does not apply over the last few years a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform ffts nuffts these rely on a mixture of interpolation and the judicious use of the fft on an oversampled grid a dutt and v rokhlin siam j sci comput 14 1993 pp 1368 1383 in this paper we observe that one of the standard interpolation or gridding schemes based on gaussians can be accelerated by a significant factor without precomputation and storage of the interpolation weights this is of particular value in two and three dimensional settings saving either 10 d n in storage in d dimensions or a factor of about 5 10 in cputime independent of dimension

anisotropic voter model a majority vote model subject to anisotropic voting rules is studied in two dimensions using a first order mean field approximation and monte carlo simulations the critical behavior is consistent with the 2d ising universality class

universality in the two dimensional continuous spin model monte carlo methods have been used to analyse the critical behaviour of the d 2 border phi 4 model which according to a recent series expansion study violates expectations based upon universality the results suggest that the model does in fact fall into the ising universality class at least as regards those parameters which characterise the critical point configurations of the ordering variable

nonequilibrium model on apollonian networks we investigate the majority vote model with two states ensuremath 1 1 and a noise parameter q on apollonian networks the main result found here is the presence of the phase transition as a function of the noise parameter q previous results on the ising model in apollonian networks have reported no presence of a phase transition we also studied the effect of redirecting a fraction p of the links of the network by means of monte carlo simulations we obtained the exponent ratio ensuremath gamma ensuremath nu ensuremath beta ensuremath nu and 1 ensuremath nu for several values of rewiring probability p the critical noise q c and u were also calculated therefore the results presented here demonstrate that the majority vote model belongs to a different universality class than equilibrium ising model on apollonian network

exact solution of the isotropic majority vote model on complete graphs the isotropic majority vote mv model which apart from the one dimensional case is thought to be nonequilibrium and violating the detailed balance condition we show that this is not true when the model is defined on a complete graph in the stationary regime the mv model on a fully connected graph fulfills the detailed balance and is equivalent to the modified ehrenfest urn model using the master equation approach we derive the exact expression for the probability distribution of finding the system in a given spin configuration we show that it only depends on the absolute value of magnetization our theoretical predictions are validated by numerical simulations

probability distribution of magnetization in the one dimensional ising model effects of boundary conditions finite size scaling functions are investigated both for the mean square magnetization fluctuations and for the probability distribution of the magnetization in the one dimensional ising model the scaling functions are evaluated in the limit of the temperature going to zero t 0 the size of the system going to infinity n while n 1 tanh j kbt is kept finite j being the nearest neighbour coupling exact calculations using various boundary conditions periodic antiperiodic free block demonstrate explicitly how the scaling functions depend on the boundary conditions we also show that the block small part of a large system magnetization distribution results are identical to those obtained for free boundary conditions

majority vote model on hyperbolic lattices we study the critical properties of a nonequilibrium statistical model the majority vote model on heptagonal and dual heptagonal lattices such lattices have the special feature that they only ca

boundary effects in a three state modified voter model for languages abstract the standard three state voter model is extended by including the outside pressure favouring one of the three language choices and by adding some biased internal noise the monte carlo simulations are motivated by states with the population divided into three groups of various affinities to each other we show the crucial influence of the boundaries for moderate lattice sizes like 500 500 by removing the fixed boundary at one side we demonstrate that this can lead to the victory of one single choice noise in contrast stabilizes the choices of all three populations in addition we compute the persistence probability i e the number of sites who have never changed their opinion during the simulation and we consider the case of rigid minded decision makers

adams operations and integral hermitian galois representations we give an algebraic interpretation of the action of the j th adams operator j on hermitian galois structure classes for tame covers of schemes of dimension 1 this generalizes work of erez and of erez taylor concerning rings of algebraic integers when j 2

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

majority vote model on triangular honeycomb and kagome lattices abstract on archimedean lattices the ising model exhibits spontaneous ordering three examples of these lattices of the majority vote model with noise are considered and studied through extensive monte carlo simulations the order disorder phase transition is observed in this system the calculated values of the critical noise parameter are q c 0 089 5 q c 0 078 3 and q c 0 114 2 for honeycomb kagome and triangular lattices respectively the critical exponents and 1 for this model are 0 15 5 1 64 5 and 0 87 5 0 14 3 1 64 3 and 0 86 6 0 12 4 1 59 5 and 1 08 6 for honeycomb kagome and triangular lattices respectively these results differ from the usual ising model results and the majority vote model on so far studied regular lattices or complex networks the effective dimensionalities of the system d eff 1 96 5 honeycomb d eff 1 92 4 kagome and d eff 1 83 5 triangular for these networks are just compatible to the embedding dimension two

the coevolution of individual economic characteristics and socioeconomic networks abstract the dynamics of individual characteristics of economic agents is modeled with the link structure influenced by this dynamics links between agents with similar characteristics are more stable than those between agents with vastly different characteristics a simple scaling law describes the number of distinct surviving characteristic realizations as a function of the number of agents and the number of possible distinct characteristics realizations with the chosen specification the investigated properties do not essentially differ from those found for analogous sociophysics models with a fixed network structure

non equilibrium ising model with competing glauber dynamics the authors consider a kinetic ising model with ferromagnetic interactions that evolves in time according to two competing glauber dynamics at different temperatures the steady states of this non equilibrium model are studied by using a dynamic pair approximation when the temperatures are low enough the system orders in a ferromagnetic state but if one of the temperatures is allowed to be negative the system may have an antiferromagnetic order they obtain the phase diagram for the case of a square lattice in this case they calculate the critical exponent v by using a mean field renormalization group method the numerical results indicate that the model falls into the same universality class of the equilibrium ising model they also show that one particular case of the non equilibrium model studied here is equivalent to the majority vote model

cumulants of the three state potts model and of nonequilibrium models with c3v symmetry the critical behaviour of two dimensional stochastic lattice gas models with c3v symmetry is analysed we study the cumulants of the order parameter for the three state equilibrium potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group c3v by means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems in particular we find that the binder reduced fourth order cumulant takes a universal value u which is the same for the three state potts model and for the irreversible models the same universal behaviour is observed for the reduced third order cumulant

critical behavior of a probabilistic cellular automaton describing a biological system we study nonequilibrium phase transitions occurring in a probabilistic cellular automaton which describes one part of the immune system in this model each site can be occupied by three type of cells and the immune response under parasitic infections is described in terms of two parameters p and r the local rules governing the evolution of this automaton possess up down symmetry similar to ising models performing monte carlo simulations on square and cubic lattices we verify that the model displays continuous kinetic phase transitions with spontaneous symmetry breaking we present detailed simulations and analysis of the critical behavior our results indicate that the model belongs to the ising universality class supporting the up down conjecture c 1998 elsevier science b v all rights reserved

computing with functions in spherical and polar geometries i the sphere a collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere functions are approximated to essentially machine precision by using a structure preserving iterative variant of gaussian elimination together with the double fourier sphere method we show that this procedure allows for stable differentiation reduces the oversampling of functions near the poles and converges for certain analytic functions operations such as function evaluation differentiation and integration are particularly efficient and can be computed by essentially one dimensional algorithms a highlight is an optimal complexity direct solver for poisson s equation on the sphere using a spectral method without parallelization we solve poisson s equation with 100 million degrees of freedom in 1 minute on a standard laptop numerical results are presented throughout in a companion paper part ii we extend the ideas presented here to computing with functions on the disk

majority vote model on a dynamic small world network abstract dynamic small world networks combine short range interactions within a fixed neighborhood with stochastic long range interactions the probability of a long range link occurring instead of a short range one is a measure of the mobility of a population here the critical properties of the majority vote model with noise on a two dimensional dynamic small world lattice are investigated via monte carlo simulation and finite size scaling analyses we construct the order disorder phase diagram and find the critical exponents associated with the continuous phase transition findings are consistent with previous results indicating that a model s transitions on static and dynamic small world networks are in the same universality class

critical behaviour of nonequilibrium three state systems the phase diagram of two different nonequilibrium three state systems is here studied by means of mfrg and computer simulations critical exponents are obtained by a finite size scaling analysis of the mc data a symmetry argument used by grinstein et al to predict the critical behaviour of two state nonequilibrium systems with up down symmetry is shown to apply to these three state systems with symmetry of interchange between two of those states

stochastic approach to equilibrium and nonequilibrium thermodynamics we develop the stochastic approach to thermodynamics based on stochastic dynamics which can be discrete master equation and continuous fokker planck equation and on two assumptions concerning entropy the first is the definition of entropy itself and the second the definition of entropy production rate which is non negative and vanishes in thermodynamic equilibrium based on these assumptions we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics these studies include the quasiequilibrium processes the convexity of the equilibrium surface the monotonic time behavior of thermodynamic potentials including entropy the bilinear form of the entropy production rate the onsager coefficients and reciprocal relations and the nonequilibrium steady states of chemical reactions

length scaling in mfrg the mean field renormalisation group mfrg has so far given poor estimates for critical indices it is argued that this can be traced to an unsatisfactory definition of the length scaling factor a new definition that improves the estimates in most cases is proposed

fast fourier transforms for nonequispaced data a group of algorithms is presented generalizing the fast fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval pi pi the schemes of this paper are based on a combination of certain analytical considerations with the classical fast fourier transform and generalize both the forward and backward ffts each of the algorithms requires o n cdot log n n cdot log 1 varepsilon arithmetic operations where varepsilon is the precision of computations and n is the number of nodes the efficiency of the approach is illustrated by several numerical examples

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

on the e constants of a variety over a finite field let x denote an irreducible smooth projective variety over a finite field which supports an action by a finite group g for each complex representation v of g we let e x g v denote the constant in the functional equation of the associated l function in this paper we study the constants e x g v when the character of the representation v is real valued our first main result shows that e x g v is positive either when the dimension d say of x is odd and v is orthogonal or when d is even and v is symplectic this then generalizes serre s theorem for the e constants of orthogonal representations for curves our second main result concerns the situation where g acts tamely on x and where the repre sentation v has real valued character is of even degree and has trivial determinant we than show that the constants e x g v are determined by certain hermitian euler characteristics associated to a stratification of x this result is particularly striking when x is a curve for then our result shows that the symplectic e constants are all determined by the virtual fp g module h ox hl ox 1 introduction let x be a regular projective variety of dimension d over a finite field k of characteristic p with q elements let k denote an algebraic closure of k and put x x x k suppose further that x carries an action by a finite group g which is tamely ramified over a divisor with strictly normal

are critical finite size scaling functions calculable from knowledge of an appropriate critical exponent critical finite size scaling functions for the order parameter distribution of the two and three dimensional ising model are investigated within a recently introduced classification theory of phase transitions the universal part of critical finite size scaling functions has been derived by employing a scaling limit which differs from the traditional finite size scaling limit in this paper the analytical predictions are compared with monte carlo simulation results we find good agreement between the analytical expression and the simulation results the agreement is consistent with the possibility that the functional form of the critical finite size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters most notably the equation of state exponent

on frohlich s conjecture for rings of integers of tame extensions where is the complex conjugate of z the constant w z is called the artin root number of in m l j martinet showed that om is not always a free zf module when n q and when f is a quaternion group of order 8 subsequently in f5 a frtihlich showed that the class of u in this special case is determined by the sign of the artin root number of the irreducible sympletic character of 2 we now return to the general case and let ci tif be the class group of locally free zf modules given a locally free 2 f module x we denote its class by x philippe cassou nogu6s defined a class t w in ci f which is defined solely in terms of the values of artin root numbers of sympletic characters this class will be defined in w after numerous computations by fr6hlich et al cf f6 c t3 for instance fr6hlich conjectured the result given below which we prove in this paper

majority vote model with a bimodal distribution of noises abstract we consider the majority vote dynamics where the noise parameter associated with each spin on a two dimensional square lattice is a bimodally distributed random variable defined as q with probability 1 f or zero with probability f where 0 f 1 is the proportion of noiseless sites we use monte carlo simulations and finite size scaling theory to characterize the ordered and disordered phases and study the phase transition of the model we conclude that in the thermodynamic limit the value of the critical noise below which there exists an ordered phase increases with f the fraction of sites with zero noise the calculation of the critical exponents shows that the introduction of disorder in the noise parameter does not alter the ising critical behavior of the model system

antiferromagnetic majority voter model on square and honeycomb lattices an antiferromagnetic version of the well known majority voter model on square and honeycomb lattices is proposed monte carlo simulations give evidence for a continuous order disorder phase transition in the stationary state in both cases precise estimates of the critical point are found from the combination of three cumulants and our results are in good agreement with the reported values of the equivalent ferromagnetic systems the critical exponents 1 1 and were found their values indicate that the stationary state of the antiferromagnetic majority voter model belongs to the ising model universality class