New Method for the Extrapolation of Finite-Size Data to Infinite Volume

TL;DR

This paper introduces a simple, effective finite-size scaling method to accurately extrapolate Monte Carlo data to infinite volume, demonstrated on various two-dimensional models, achieving high precision even with large correlation lengths.

Contribution

The paper presents a novel finite-size scaling technique for extrapolating Monte Carlo data to infinite volume, with careful analysis of errors and broad applicability.

Findings

Reliable extrapolations with errors of a few percent

Effective even when correlation length exceeds lattice size by 1000 times

Validated on three different two-dimensional models

Abstract

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $\sigma$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.