Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling

TL;DR

This paper introduces a covariance-optimized finite-size scaling method for Monte Carlo data that reduces statistical errors by exploiting covariance between observables, demonstrated effectively in the Ising model.

Contribution

The paper presents a novel covariance-based optimization technique for finite-size scaling analysis that improves accuracy without extra computational cost.

Findings

Significant reduction in statistical errors in Monte Carlo estimates.

Large gain factors in CPU time for Ising model simulations.

Method applicable generally without additional computational overhead.

Abstract

In the finite-size scaling analysis of Monte Carlo data, instead of computing the observables at fixed Hamiltonian parameters, one may choose to keep a renormalization-group invariant quantity, also called phenomenological coupling, fixed at a given value. Within this scheme of finite-size scaling, we exploit the statistical covariance between the observables in a Monte Carlo simulation in order to reduce the statistical errors of the quantities involved in the computation of the critical exponents. This method is general and does not require additional computational time. This approach is demonstrated in the Ising model in two and three dimensions, where large gain factors in CPU time are obtained.