Mean-value identities as an opportunity for Monte Carlo error reduction

TL;DR

This paper proposes using exact mean-value identities as control variates in Monte Carlo simulations to reduce statistical errors, demonstrated effectively in the 2D Ising model at criticality with significant CPU efficiency gains.

Contribution

It introduces a simple, general method to exploit mean-value identities as control variates for error reduction in Monte Carlo simulations.

Findings

CPU gain factor between 2 and 4 in the 2D Ising model

Method is simple, general, and cost-effective

Effective in reducing statistical errors in Monte Carlo simulations

Abstract

In the Monte Carlo simulation of both Lattice field-theories and of models of Statistical Mechanics, identities verified by exact mean-values such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well known and sensitive tests of thermalization bias as well as checks of pseudo random number generators. We point out that they can be further exploited as "control variates" to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the two dimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.