Related papers: Wang-Landau sampling: Improving accuracy
Wang and Landau proposed recently, a simple and flexible non-Boltzmann Monte Carlo method for estimating the density of states, from which the macroscopic properties of a closed system can be calculated. They demonstrated their algorithm by…
We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128,000 approx. 503 sites which are linked together according to the Voronoi/Delaunay prescription. For each…
In this contribution we apply a new variant of the density of states method to the Z3 spin model at finite density. We use restricted expectation values evaluated with Monte Carlo simulations and study their dependence on a control…
We revisit the nature of the quasi-one-dimensional Ising model on the basis of Wang-Landau simulation. We introduce the density of states in the two-dimensional energy space corresponding to the intra- and inter-chain directions. We then…
Mean field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from…
Flat-histogram Monte Carlo simulations are well-established, robust methods to perform random walks in a physical observable or parameter space, making them suitable for finding ground states or studying phase transitions in complex systems…
The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising…
The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
We present a new Monte Carlo algorithm applying a history-driven mechanism for the calculation of the density of states for classical statistical models. The new method is as efficient as the Wang-Landau method in sampling through the…
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
The density of never changed opinions during the Sznajd consensus-finding process decays with time t as 1/t^{theta}. We find theta ~= 3/8 for a chain, compatible with the exact Ising result of Derrida et al. In higher dimensions, however,…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
The two-magnon-bound-state mass gap m_2 for the two-dimensional quantum Ising model was investigated by means of the numerical diagonalization method; the low-lying spectrum is directly accessible via the numerical diagonalization method.…
In any valid Monte Carlo sampling that realizes microcanonical property we can collect statistics for a transition matrix in energy. This matrix is used to determine the density of states, from which most of the thermodynamical averages can…
The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
We implement the Wang-Landau algorithm in the context of SU(N) lattice gauge theories. We study the quenched, reduced version of the lattice theory and calculate its density of states for N=20,30,40,50. We introduce a variant of the…
A simple modification of the ``Wang-Landau sampling'' algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm.