Implementation of the histogram method for equilibrium statistical models using moments of a distribution

TL;DR

This paper introduces a simplified histogram method for Monte Carlo extrapolations that leverages moments of operators instead of histograms, enabling efficient calculations for models like the 2-D Ising model.

Contribution

It presents a novel implementation of the Histogram Method using moments, reducing memory requirements for extrapolations in statistical models.

Findings

Effective for multiple operator extrapolations

Reduces memory usage in Monte Carlo simulations

Applicable to 2-D Ising model

Abstract

This paper shows a simple implementation of the Histogram Method for extrapolations in Monte Carlo simulations, using the moments of the operators that define the energy, instead of their histogram. This implementation is suitable for extrapolation over several operators, a type of calculation that is hindered by computer memory limitations. Examples of this approach are given for the 2-D Ising model.