Ising Model Universality for Two-Dimensional Lattices

TL;DR

This study uses Monte Carlo simulations and finite-size scaling to demonstrate that the critical exponents of the two-dimensional Ising model on random Delaunay lattices match those on regular lattices, confirming universality.

Contribution

It provides the first comprehensive numerical evidence that the Ising model's universality extends to two-dimensional random lattices.

Findings

Critical exponents match those of regular lattices

Universality holds for two-dimensional Ising model on random lattices

Finite-size scaling confirms theoretical predictions

Abstract

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80\,000 sites. By applying reweighting techniques and finite-size scaling analyses to time-series data near criticality, we obtain unambiguous support that the critical exponents for the random lattice agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.