Corrections to finite-size scaling in the 3D Ising model based on non-perturbative approaches and Monte Carlo simulations

TL;DR

This paper investigates corrections to finite-size scaling in the 3D Ising model using non-perturbative analytical methods and Monte Carlo simulations, providing new estimates for correction exponents and discussing their impact on critical exponent determination.

Contribution

It introduces a non-perturbative approach to estimate correction-to-scaling exponents and analyzes the dependence of these estimates on different finite-size scaling methods.

Findings

Correction exponent (gamma-1)/nu is approximately 0.38.

Numerical estimate of omega is 0.25(33), consistent with theoretical bounds.

Estimates of omega vary significantly across methods, affecting critical exponent calculations.

Abstract

Corrections to scaling in the 3D Ising model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L. Analytical arguments show the existence of corrections with the exponent (gamma-1)/nu (approximately 0.38), the leading correction-to-scaling exponent being omega =< (gamma-1)/nu. A numerical estimation of omega from the susceptibility data within 40 =< L =< 2048 yields omega=0.25(33). It is consistent with the statement omega =< (gamma-1)/nu, as well as with the value omega = 1/8 of the GFD theory. We reconsider the MC estimation of omega from smaller lattice sizes to show that it does not lead to conclusive results, since the obtained values of omega depend on the particular method chosen. In particular, estimates ranging from omega =1.274(72) to omega=0.18(37) are obtained by four different finite-size scaling methods, using MC data for thermodynamic average quantities, as well as for partition function zeros. We discuss the influence of omega on the estimation of exponents eta and nu.