The Critical Finite Size Scaling Relation of the Order-Parameter Probability Distribution for the Three-Dimensional Ising Model on the Creutz Cellular Automaton

TL;DR

This paper investigates the finite size scaling of the order parameter distribution at criticality for 3D Ising models using Creutz cellular automaton simulations, confirming theoretical relations and estimating critical exponents.

Contribution

It verifies the finite size scaling relation for the order parameter distribution and estimates the critical exponent  using cellular automaton simulations.

Findings

Finite size scaling relation is numerically verified.

Critical exponent  estimated consistent with Monte Carlo results.

Method demonstrates effectiveness of cellular automata in critical phenomena analysis.

Abstract

We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice with periodic boundary conditions. The finite size scaling relation for the order parameter probability distribution is tested and verified numerically by microcanonical Creutz cellular automata simulations. The state critical exponent \delta, which characteries the far tail regime of the scaling order parameter probability distribution, is estimated for 3-d Ising models using the cellular automaton simulations at the critical temperature. The results are in good agreement with the monte carlo calculations.