Metropolis and Wang-Landau Algorithms

TL;DR

This paper discusses the Metropolis algorithm for mechanical property estimation and introduces the Wang-Landau algorithm for calculating both mechanical and thermal properties of equilibrium systems.

Contribution

It provides a pedagogical overview of the Metropolis and Wang-Landau algorithms, highlighting their roles in estimating different thermodynamic properties.

Findings

Metropolis algorithm effectively estimates mechanical properties.

Wang-Landau algorithm enables calculation of thermal properties.

Comparison of algorithms for different property estimations.

Abstract

Metropolis algorithm has been extensively employed for simulating a canonical ensemble and estimating macroscopic properties of a closed system at any desired temperature. A mechanical property, like energy can be calculated by averaging over a large number of micro states of the stationary Markov chain generated by the Metropolis algorithm. However thermal properties like entropy, and free energies are not easily accessible. A method called umbrella sampling was proposed some forty years ago for this purpose. Ever since, umbrella sampling has undergone several metamorphoses and we have now multi canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc. In these talks I shall tell you of Metropolis algorithm for estimating mechanical properties and of Wang-Landau algorithm for estimating both mechanical and thermal properties of an equilibrium system. I shall make these lectures as pedagogical and self-contained as possible.