Efficient method of finding scaling exponents from finite-size Monte-Carlo simulations

TL;DR

This paper introduces a novel Monte-Carlo simulation technique that improves the accuracy of estimating scaling exponents in complex systems by effectively addressing finite-size effects and asymptotic corrections.

Contribution

The paper presents a new method for finite-size scaling analysis that reduces uncertainties and enables determination of asymptotic correction exponents.

Findings

More accurate scaling exponents obtained for percolation cluster hulls

Method reduces uncertainties in finite-size scaling estimates

Able to determine exponents of asymptotic corrections

Abstract

Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique of dealing with the problem of finite-size scaling. This new method allows not only to decrease the uncertainties of the scaling exponents, but makes it also possible to determine the exponents of the asymptotic corrections to the scaling laws. The efficiency of the technique is demonstrated by finding the scaling exponent of uncorrelated percolation cluster hulls.