Broad Histogram Method

TL;DR

This paper introduces a novel histogram method that directly measures the degeneracy of energy states using a non-biased random walk, overcoming limitations of traditional methods that rely on Boltzmann distributions.

Contribution

The paper presents a new approach for estimating energy degeneracies using a power-law decay random walk, which is model-independent and exact for 1D Ising models.

Findings

Method is exact for 1D Ising ferromagnet

Numerical results agree well with exact solutions for 2D Ising model

Overcomes narrow temperature window limitations of traditional methods

Abstract

Ferrenberg and Swendsen histogram method is based on Boltzmann probability distribution which presents exponentially decaying tails. Thus, it gives accurate measures only within a narrow window around the simulated temperature. The larger the system, the narrower this window, and the worst the performance of this method. We present a quite different approach, defining a non-biased random walk along the E axis with long range power-law decaying tails, and measuring directly the degeneracy g(E), without thermodynamic constraints. Our arguments are general (model independent), and the method is shown to be exact for the 1D Ising ferromagnet. Also for the 2D Ising ferromagnet, our numerical results for different thermodynamic quantities agree quite well with exact expressions.