on the application of the critical minimum energy subspace method to disordered systems abstract we discuss the recent application to strongly disordered systems of the critical minimum energy subspace crmes method used to limit the energy subspace of the wang landau sampling we compare with our results on the 3d random field ising model obtained by a multi range wang landau simulation over the whole energy range we point out some problems that may arise when applying the crmes scheme to models having a complex free energy landscape

effects of random and deterministic discrete scale invariance on the critical behavior of the potts model the effects of disorder on the critical behavior of the q state potts model in noninteger dimensions are studied by comparison of deterministic and random fractals sharing the same dimensions in the framework of a discrete scale invariance we carried out intensive monte carlo simulations in the case of a fractal dimension slightly smaller than two d f 1 974636 we give evidence that the disorder structured by discrete scale invariance does not change the first order transition associated with the deterministic case when q 7 furthermore the study of the high value q 14 shows that the transition is a second order one both for deterministic and random scale invariance but that their behavior belongs to different university classes

numerical determination of the distribution of energies for the xy model abstract we compute numerically the distribution of energies e n for the xy model with short and long range interactions we find that in both cases the distribution can be fitted to the functional form e n exp n e n with e n an intensive function of the energy

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

optimal monte carlo updating based on peskun s theorem it is shown that optimal transition matrices in markov chain monte carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight we will compare the statistical efficiency of this sampler to existing algorithms such as heat bath updating and the metropolis algorithm we provide numerical results for the potts model as an application in classical physics as an application in quantum physics we consider the spin 3 2xy model and the bose hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework

semiclassical chaos in atomic clusters an exploration with ring polymer molecular dynamics the ring polymer molecular dynamics rpmd method was recently shown to provide a powerful framework to address the time evolution of many particle semiclassical systems its underlying hamiltonian formulation is exploited here to define and compute some measures of deterministic chaos namely the lyapunov characteristic exponent applications are presented for weakly bound neon clusters with the aim of assessing the influence of nuclear delocalization on the nonlinear dynamics it is found that the balance between the additional degrees of freedom in the rpmd description and the harmonic nature of the additional interactions leads to more regular dynamics at high temperature but more chaotic dynamics at low temperature intrinsic features of quantum effects on the isomerization dynamics also have a signature on the lyapunov exponent

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

monte carlo study of the triangular blume capel model under bond randomness the effects of bond randomness on the universality aspects of a two dimensional d 2 blume capel model embedded in the triangular lattice are discussed the system is studied numerically in both its first and second order phase transition regimes by a comprehensive finite size scaling analysis for a particularly suitable value of the disorder strength we find that our data for the second order phase transition emerging under random bonds from the second order regime of the pure model are compatible with the universality class of the two dimensional 2d random ising model furthermore we find evidence that the second order transition emerging under bond randomness from the first order regime of the pure model belongs again to the same universality class although the first finding reinforces the scenario of strong universality in the 2d ising model with quenched disorder the second is in difference from the critical behavior emerging under randomness in the cases of the ex first order transitions of the potts model finally our results verify previous renormalization group calculations on the blume capel model with disorder in the crystal field coupling

multiparticle random walks on a deformable medium multiparticle random walks on a deformable medium have been investigated in 2 1 dimensions the time evolution of the particle distribution is studied the results show that the randomly distributed particles in the beginning will be self organized into a cluster pattern in the intermediate stage and then return to the random distribution pattern in the late stage the dependence of the clustering degree on the stiffness parameter of medium ensuremath alpha stability parameter of systems ensuremath beta and average particle density ensuremath rho 0 is also investigated there exists an optimal clustering stability ensuremath beta p at which the system has the strongest clustering ability and corresponds to a maximum clustering coefficient ensuremath gamma p the dependence of the optimal clustering coefficient ensuremath gamma p on the stiffness ensuremath alpha and particle density ensuremath rho 0 is obtained and the landscape of the medium generated by particles is also investigated

monte carlo study of the antiferromagnetic three state potts model with a staggered polarization field on the square lattice using the wang landau monte carlo method we study the antiferromagnetic af three state potts model with a staggered polarization field on the square lattice we obtain two phase transitions one belongs to the ferromagnetic three state potts universality class and the other to the ising universality class the phase diagram obtained is quantitatively consistent with the transfer matrix calculation the ising transition in the large nearest neighbour interaction limit has been made clear by the detailed analysis of the energy density of states

entropic sampling of simple polymer models within wang landau algorithm in this paper we apply a new simulation technique proposed in wang and landau wl 2001 phys rev lett 86 2050 to sampling of three dimensional lattice and continuous models of polymer chains distributions obtained by homogeneous unconditional random walks are compared with results of entropic sampling es within the wl algorithm while homogeneous sampling gives reliable results typically in the range of 4 5 orders of magnitude the wl entropic sampling yields them in the range of 20 30 orders and even larger with comparable computer effort a combination of homogeneous and wl sampling provides reliable data for events with probabilities down to 10 35 for the lattice model we consider both the athermal case self avoiding walks saws and the thermal case when an energy is attributed to each contact between nonbonded monomers in a self avoiding walk for short chains the simulation results are checked by comparison with the exact data in wl calculations for chain lengths up to n 300 scaling relations for saws are well reproduced in the thermal case distribution over the number of contacts is obtained in the n range up to n 100 and the canonical averages internal energy heat capacity excess canonical entropy mean square end to end distance are calculated as a result in a wide temperature range the continuous model is studied in the athermal case by sorting conformations of a continuous phantom freely joined n bonded chain with a unit bond length over a stochastic variable the minimum distance between nonbonded beads we determine the probability distribution for the n bonded chain with hard sphere monomer units over its diameter a in the complete diameter range 0 a 2 within a single es run this distribution provides us with excess specific entropy for a set of diameters a in this range calculations were made for chain lengths up to n 100 and results were extrapolated to n for a in the range 0 a 1 25

novel monte carlo algorithms and their applications abstract we describe a generalized scheme for the probability changing cluster pcc algorithm based on the study of the finite size scaling property of the correlation ratio the ratio of the correlation functions with different distances we apply this generalized pcc algorithm to the two dimensional 6 state clock model we also discuss the combination of the cluster algorithm and the extended ensemble method we derive a rigorous broad histogram relation for the bond number a monte carlo dynamics based on the number of potential moves for the bond number is proposed and applied to the three dimensional ising and 3 state potts models

large deviations of connected components in the stochastic block model we study the stochastic block model which is often used to model community structures and study community detection algorithms we consider the case of two blocks in regard to its largest connected component and largest biconnected component respectively we are especially interested in the distributions of their sizes including the tails down to probabilities smaller than 10 ensuremath 800 for this purpose we use sophisticated markov chain monte carlo simulations to sample graphs from the stochastic block model ensemble we use these data to study the large deviation rate function and conjecture that the large deviation principle holds further we compare the distribution to the well known erd ifmmode mbox h o else h o fi s r enyi ensemble where we notice subtle differences at and above the percolation threshold

yang lee zeros of triangular ising antiferromagnets abstract in our previous research by combining both the exact enumeration method microcanonical transfer matrix for a small system l 9 with the wang landau monte carlo algorithm for large systems to l 30 we obtained the exact and approximate densities of states g m e as a function of the magnetization m and exchange energy e for a triangular lattice ising model in this paper based on the density of states g m e the precise distribution of the yang lee zeros of triangular lattice ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature a e 2 for a 9 9 lattice system also the feasibility of the yang lee zero approach combined with the wang landau algorithm is demonstrated as a result we obtained the magnetic exponents for triangular ising antiferromagnets at various temperatures

on the relation between projections of the reweighted path ensemble we derive several distribution functions for the recently introduced reweighted path ensemble rogal et al in j chem phys 133 174109 2010 the configurational and path densities the reactive current and the generalized committors for the different path types we relate these distributions to the free energy and to the expressions for the rate constant in the transition state theory the reactive flux method the transition path interface sampling framework and the bayesian path statistics in addition we compute the transmission coefficient distribution from the reweighted path ensemble finally we derive the path sampling shooting point distributions for a simple two dimensional langevin model we illustrate how these novel distributions can be used as analysis tools in rare event simulations

a null model for dunbar s circles abstract an individual s social group may be represented by their ego network formed by the links between the individual and their acquaintances ego networks present an internal structure of increasingly large nested layers or circles of decreasing relationship intensity whose size exhibits a precise scaling ratio starting from the notion of limited social bandwidth and assuming fixed costs for the links in each layer we propose a null model built on a grand canonical ensemble that generates the observed hierarchical social structure the observed internal structure of ego networks becomes a natural outcome to expect when we assume the existence of layers demanding different amounts of resources in the thermodynamic limit reached when the number of ego network copies is large the specific layer degrees follow a poisson distribution we also find that under certain conditions equispaced layer costs are necessary to obtain a constant group size scaling our model presents interesting analogies to a bose einstein gas that we briefly discuss finally we fit and compare the model with an empirical social network

temperature measurement from perturbations the notion of configuration temperature is extended to discontinuous systems by identifying the temperature as the nontrivial root of several integral equations regarding the distribution of the energy change upon configuration perturbations the relations are generalized to pressure and a distribution mean force

momentum shell renormalization group flow from simulation our recently developed fourier monte carlo algorithm permits a nonperturbative calculation of momentum shell renormalization group flows by simulation which despite its apparent simplicity is illustrative both numerically as well as conceptually interesting we study the example of a varphi 4 model with long range lattice interaction for this model we show that the topology of the renormalization flow is globally accessible in a particularly convenient way the nontrivial fixed point of wilson fisher type is observed its accompanying critical exponents are numerically determined from fitting its surrounding flow pattern to a linearized renormalization group transformation the results are compared to those obtained from perturbation theory expansion and earlier monte carlo simulations application of our method is also expected to be rewarding in other models with long range interactions

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

entropic sampling in the path integral monte carlo method we have extended the entropic sampling monte carlo method to the case of path integral representation of a quantum system a two dimensional density of states is introduced into path integral form of the quantum canonical partition function entropic sampling technique within the algorithm suggested recently by wang and landau wang f and landau d p 2001 phys rev lett 86 2050 is then applied to calculate the corresponding entropy distribution a three dimensional quantum oscillato ri sc onsidered as an example canonical distributions for a wide range of temperatures are obtained in a single simulation run and exact data for the energy are reproduced

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

optimal stability estimates for continuity equations this review paper is concerned with the stability analysis of the continuity equation in the diperna lions setting in which the advecting velocity field is sobolev regular quantitative estimates for the equation were derived only recently but optimality was not discussed we revisit the results from our 2017 paper compare the new estimates with previously known estimates for lagrangian flows and demonstrate how these can be applied to produce optimal bounds in applications from physics engineering and numerical analysis

improving samc using smoothing methods theory and applications to bayesian model selection problems stochastic approximation monte carlo samc has recently been proposed by liang liu and carroll j amer statist assoc 102 2007 305 320 as a general simulation and optimization algorithm in this paper we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to bayesian model selection problems the new algorithm is tested through a change point identification example the numerical results indicate that the new algorithm can outperform samc and reversible jump mcmc significantly for the model selection problems the new algorithm represents a general form of the stochastic approximation markov chain monte carlo algorithm it allows multiple samples to be generated at each iteration and a bias term to be included in the parameter updating step a rigorous proof for the convergence of the general algorithm is established under verifiable conditions this paper also provides a framework on how to improve efficiency of monte carlo simulations by incorporating some nonparametric techniques

ensemble inhibition and excitation in the human cortex an ising model analysis with uncertainties the pairwise maximum entropy model also known as the ising model has been widely used to analyze the collective activity of neurons however controversy persists in the literature about seemingly inconsistent findings whose significance is unclear due to lack of reliable error estimates we therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive markov chain monte carlo after the convergence of the main optimization algorithm we apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake sleep cycle our analysis shows that the ising model captures neuronal collective behavior much better than the independent model during wakefulness light sleep and deep sleep when both excitatory e and inhibitory i neurons are modeled ignoring the inhibitory effects of i neurons dramatically overestimates synchrony among e neurons furthermore information theoretic measures reveal that the ising model explains about 80 95 of the correlations depending on sleep state and neuron type thermodynamic measures show signatures of criticality although we take this with a grain of salt as it may be merely a reflection of long range neural correlations

structure and stability of isotropic states of hard platelet fluids we study the thermodynamics and the pair structure of hard infinitely thin circular platelets in the isotropic phase monte carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function including nonmonotonical variation of some of the components with density integral equation theory is shown to reproduce the main features observed in simulations the hypernetted chain closure as well as its extended versions that include the bridge function up to second and third order in density perform better than both the percus yevick closure and verlet bridge function approximation using a recent fundamental measure density functional theory an analytic expression for the direct correlation function is obtained as the sum of the mayer bond and a term proportional to the density and the intersection length of two platelets this is shown to give a reasonable estimate of the structure found in simulations but to fail to capture the nonmonotonic variation with density we also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the kerr coefficient vanishes as a reference system we compare to simulation results for hard oblate spheroids with small but nonzero elongations demonstrating that the case of vanishingly thin platelets is approached smoothly

flat histogram monte carlo simulations of triangulated fixed connectivity surface models using the wang landau flat histogram monte carlo fhmc simulation technique we were able to study two types of triangulated spherical surface models in which the two dimensional extrinsic curvature energy is assumed in the hamiltonian the gaussian bond potential is also included in the hamiltonian of the first model but it is replaced by a hard wall potential in the second model the results presented in this paper are in good agreement with the results previously reported by our group the transition of surface fluctuations and collapsing transition were studied using the canonical metropolis monte carlo simulation technique and were found to be of the first order the results obtained in this paper also show that the fhmc technique can be successfully applied to triangulated surface models it is non trivial whether the technique is applicable or not to surface models because the simulations are performed on relatively large surfaces

improving the efficiency of monte carlo simulations of systems that undergo temperature driven phase transitions recently velazquez and curilef proposed a methodology to extend monte carlo algorithms based on a canonical ensemble which aims to overcome slow sampling problems associated with temperature driven discontinuous phase transitions we show in this work that monte carlo algorithms extended with this methodology also exhibit a remarkable efficiency near a critical point our study is performed for the particular case of a two dimensional four state potts model on a square lattice with periodic boundary conditions this analysis reveals that the extended version of metropolis importance sampling is more efficient than the usual swendsen wang and wolff cluster algorithms these results demonstrate the effectiveness of this methodology to improve the efficiency of mc simulations of systems that undergo any type of temperature driven phase transition

a comparison between broad histogram and multicanonical methods we discuss the conceptual differences between the broad histogram bhm and reweighting methods in general and particularly the so called multicanonical muca approaches the main difference is that bhm is based on microcanonical fixed energy averages which depend only on the good statistics taken inside each energy level the detailed distribution of visits among different energy levels determined by the particular dynamic rule one adopts is irrelevant contrary to muca where the results are extracted from the dynamic rule itself within bhm any microcanonical dynamics could be adopted as a numerical test we have used both bhm and muca in order to obtain the spectral energy degeneracy of the ising model in 4 4 4 and 32 32 lattices for which exact results are known we discuss why bhm gives more accurate results than muca even using the same markovian sequence of states in addition such an advantage increases for larger systems

a binomial approximation method for the ising model a large portion of the computation required for the partition function of the ising model can be captured with a simple formula in this work we support this claim by defining an approximation to the partition function and other thermodynamic quantities of the ising model that requires no algorithm at all this approximation which uses the high temperature expansion is solely based on the binomial distribution and performs very well at low temperatures at high temperatures we provide an alternative approximation which also serves as a lower bound on the partition function and is trivial to compute we provide theoretical evidence and the results of numerical experiments to support the strength of these approximations

common coupled fixed point results for probabilistic φ contractions in menger spaces abstract several hybrid probabilistic contractions with a gauge function are considered using the properties of the pseudo metric and the triangular norm some common coupled fixed point theorems are obtained in complete menger probabilistic metric spaces the main results are general because they do not assume any continuity or monotonicity conditions for