Single-Cluster Monte Carlo Study of the Ising Model on Two-Dimensional Random Lattices

TL;DR

This study uses Monte Carlo simulations on random lattices to verify that the critical behavior of the 2D Ising model matches that of regular lattices, confirming universality in disordered systems.

Contribution

It demonstrates that the critical exponents of the 2D Ising model on random lattices agree with those on regular lattices, supporting universality in disordered systems.

Findings

Critical exponents match those of regular lattices

Universality holds for the 2D Ising model on random lattices

Finite-size scaling confirms critical behavior

Abstract

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80,000 sites which are linked together according to the Voronoi/Delaunay prescription. In one set of simulations we use reweighting techniques and finite-size scaling analysis to investigate the critical properties of the model in the very vicinity of the phase transition. In the other set of simulations we study the approach to criticality in the disordered phase, making use of improved estimators for measurements. From both sets of simulations we obtain clear evidence that the critical exponents agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.