Broad Histogram Monte Carlo

TL;DR

This paper introduces a novel Monte Carlo method that efficiently estimates energy state degeneracies, enabling accurate thermodynamic calculations over wider temperature ranges than traditional techniques.

Contribution

The paper presents a new histogram Monte Carlo technique that produces broader histograms, improving accuracy and efficiency in thermodynamic property estimation.

Findings

More accurate results for 2D Ising model

Efficient reconstruction of thermodynamic functions

Successful application to 3D Ising and spin glass models

Abstract

We propose a new Monte Carlo technique in which the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations. The obtained histograms are much broader than those of the canonical histogram technique studied by Ferrenberg and Swendsen. Thus we can reliably reconstruct thermodynamic functions over a much larger temperature scale also away from the critical point. We show for the two-dimensional Ising model how our new method reproduces exact results more accurately and using less computer time than the conventional histogram method. We also show data in three dimensions for the Ising ferromagnet and the Edwards Anderson spin glass.