A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class

TL;DR

This study uses extensive finite size scaling simulations of the 3D Ising and Blume-Capel models to precisely estimate critical exponents, employing improved observables and focusing on parameters with minimal correction amplitudes.

Contribution

It provides highly accurate estimates of critical exponents for 3D lattice models using advanced finite size scaling techniques and improved observables.

Findings

Estimated critical exponents: nu=0.63002(10), eta=0.03627(10), omega=0.832(6)

Results are consistent with previous Monte Carlo, series expansions, and field theory studies

Enhanced precision in critical exponent determination for 3D Ising universality class.

Abstract

We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates for critical exponents. We focus on values of D, where the amplitudes of leading corrections are small. Furthermore we employ improved observables that have a small amplitude of the leading correction. We obtain nu=0.63002(10), eta=0.03627(10) and omega=0.832(6). We compare our results with those obtained from previous Monte Carlo simulations and high temperature series expansions of lattice models, by using field theoretic methods and experiments.