Simulation via Direct Computation of Partition Functions

TL;DR

This paper introduces a flexible and efficient simulation method that computes partition functions directly, enabling the study of complex systems with rugged energy landscapes across various macroscopic conditions.

Contribution

It presents a novel, scalable approach using histogram flattening and the Wang-Landau scheme for direct partition function computation applicable to diverse ensembles.

Findings

Efficient simulation of large Ising models.

Successful identification of protein ground states.

Study of liquid-vapor phase transitions.

Abstract

In this paper, we demonstrate the efficiency of simulations via direct computation of the partition function under various macroscopic conditions, such as different temperatures or volumes. The method can compute partition functions by flattening histograms, through the Wang-Landau recursive scheme, outside the energy space. This method offers a more general and flexible framework for handling various types of ensembles, especially the ones in which computation of the density of states is not convenient. It can be easily scaled to large systems, and it is flexible in incorporating Monte Carlo cluster algorithms or molecular dynamics. High efficiency is shown in simulating large Ising models, in finding ground states of simple protein models, and in studying the liquid-vapor phase transition of a simple fluid. The method is very simple to implement and we expect it to be efficient in studying complex systems with rugged energy landscapes, e.g., biological macromolecules.