Related papers: Convergence of the Wang-Landau algorithm
We describe the study of thermodynamics of materials using replica-exchange Wang-Landau (REWL) sampling, a generic framework for massively parallel implementations of the Wang-Landau Monte Carlo method. To evaluate the performance and…
We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting…
The statistical significance of network properties is conditioned on null models which satisfy spec- ified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such…
As far as we know, there is no flat-histogram algorithm to sample the stationary distribution of non-equilibrium stochastic processes. The present work addresses this gap by introducing a generalization of the Wang-Landau algorithm, applied…
We show how the well-known Wang-Landau method can be modified to produce non-flat distributions. Through the choice of a suitable profile this can lead to an increase in efficiency for some systems. Examples for such an enhancement are…
Monte Carlo simulation using a combination of Wang Landau (WL) and Transition Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with continuous energy is described. One of the models, the one dimensional Lebwohl-Lasher…
Combining traditional Wang-Landau sampling for multiple replica systems with an exchange of densities of states between replicas, we describe a general framework for simulations on massively parallel Petaflop supercomputers. The advantages…
We propose a new numerical method to determine the central charge of the conformal field theory models corresponding to the 2D lattice models. In this method, the free energy of the lattice model on the torus is calculated by the…
We explain the fundamental challenges of sampling from multimodal distributions, particularly for high-dimensional problems. We present the major types of MCMC algorithms that are designed for this purpose, including parallel tempering,…
The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of…
Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) are shown to…
Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…
In this short note, we show how the parallel adaptive Wang-Landau (PAWL) algorithm of Bornn et al. (2013) can be used to automate and improve simulated tempering algorithms. While Wang-Landau and other stochastic approximation methods have…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
We propose a general method (based on the Wang-Landau algorithm) to compute numerically free energies that are obtained from the logarithm of the ratio of suitable partition functions. As an application, we determine with high accuracy the…
Monte Carlo algorithms such as the Wang-Landau algorithm and similar `entropic' methods are able to accurately sample the density of states of model systems and thereby give access to thermal equilibrium properties at any temperature.…
When performing a Monte Carlo calculation, the running time should in principle be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its…
In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard…
We present modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states $g(M,E)$ of ferromagnet Heisenberg models. The joint density of…
A methodology for calculating the contribution of charged defects to the configurational free energy of an ionic crystal is introduced. The temperature-independent Wang-Landau Monte Carlo technique is applied to a simple model of a solid…