A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling

Abstract

We describe a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states. The probability can be computed at any temperature by weighting the density of states by the appropriate Boltzmann factor. Thermodynamic properties can be determined from suitable derivatives of the partition function and, unlike ''standard'' methods, the free energy and entropy can also be computed directly. To demonstrate the simplicity and power of the algorithm, we apply it to models exhibiting first-order or second-order phase transitions.

Developments in Wang-Landau simulations of a simple continuous homopolymer

“…Wang-Landau sampling is a Monte Carlo technique that was developed as a temperature independent, iterative method with the ability to sample rough energy landscapes [5,14]. The technique was originally implemented for discrete models [3], and in order to perform simulations of a continuous model a few issues must be addressed.…”

Thermodynamic properties and correlation functions of Ar films on the surface of a bundle of nanotubes

“…Two Markov Chain Monte Carlo simulation methods were used, the Metropolis algorithm 28,29 and the WangLandau algorithm. 30,31,32 The Metropolis algorithm was used to calculate configurational observables, such as density distributions and correlation functions. The Wang-Landau algorithm was used to calculate thermodynamic observables expressible in terms of ensemble averages or their derivatives, such as specific and isosteric heat, for certain N ; the Metropolis algorithm was used to determine the full N dependence.…”

Thermodynamics of Ising model on the kagome lattice

“…Для исследования модели нами использован алгоритм Ванга-Ландау метода Мон-те-Карло [5][6][7][8][9][10][11][12][13][14][15]. Данный алгоритм позволяет найти функцию плотности состояний си-стемы, зная которую можно легко рассчитать все остальные характеристики системы.…”