Corrections to scaling in the 3D Ising model: a comparison between MC and MCRG results

TL;DR

This study investigates corrections to scaling in the 3D Ising model using large-scale Monte Carlo simulations, comparing results with Monte Carlo renormalization group estimates and providing stable critical exponent values.

Contribution

It provides new Monte Carlo estimates of correction-to-scaling exponent omega and compares them with MCRG results, discussing potential transient behaviors and refining analysis methods.

Findings

Estimated omega decreases when smaller lattices are discarded

MC critical exponents eta and nu are stable and agree with conformal bootstrap results

Discussion on whether omega is truly smaller or reflects transient behavior

Abstract

Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to L=3456. Our estimated values of the correction-to-scaling exponent omega tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e., omega about 0.7 and omega = 0.75(5). We discuss the possibilities that omega is either really smaller than usually expected or these values of omega describe some transient behavior. We propose refining MCRG simulations and analysis to resolve this issue. In distinction from omega, our actual MC estimations of the critical exponents eta and nu provide stable values eta=0.03632(13) and nu=0.63017(31), which well agree with those of the conformal bootstrap method, i.e., eta=0.0362978(20) and nu=0.6299709(40).