Properties of iterative Monte Carlo single histogram reweighting

TL;DR

This paper introduces an iterative Monte Carlo method that combines histogram reweighting and linear filtering to efficiently locate critical points in models like the 2D Ising model, providing insights into error analysis and temperature fluctuations.

Contribution

The paper presents a novel iterative Monte Carlo algorithm that attracts the temperature to critical points using combined reweighting and filtering techniques, with a stochastic model for analysis.

Findings

The iterative algorithm converges to a stationary distribution near the pseudocritical temperature.

The stochastic autoregressive model explains the error behavior of histogram reweighting.

A simple relation links variance of pseudocritical temperature to filtering parameters.

Abstract

We present iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The 2d Ising model of ferromagnet is studied numerically as an illustration. In that case, the iterations uncovered stationary regime with invariant probability distribution function of temperature which is peaked nearly the pseudocritical temperature of specific heat. The sequence of generated temperatures is analyzed in terms of stochastic autoregressive model. The error of histogram reweighting can be better understood within the suggested model. The presented model yields a simple relation, connecting variance of pseudocritical temperature and parameter of linear filtering.