Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model

TL;DR

This paper advances Monte Carlo simulation techniques to precisely determine the critical temperature and correlation length exponent of the 3d Ising model, surpassing previous estimates in accuracy.

Contribution

It introduces enhanced Monte Carlo methods with advanced data analysis to achieve unprecedented precision in critical parameter estimation for the 3d Ising model.

Findings

Critical inverse temperature Kc = 0.221654626(5)

Correlation length exponent ν = 0.629912(86)

Precision exceeds all previous Monte Carlo estimates

Abstract

While the 3d Ising model has defied analytic solution, various numerical methods like Monte Carlo, MCRG and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g. logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc = 0.221 654 626(5) and the critical exponent of the correlation length {\nu} = 0.629 912(86) with precision that exceeds all previous Monte Carlo estimates.