Ising model on 3D random lattices: A Monte Carlo study

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the Ising model on 3D random lattices, finding results consistent with those on regular lattices, thus supporting universality.

Contribution

First comprehensive Monte Carlo analysis of the Ising model on 3D random lattices, demonstrating universality of critical exponents across lattice types.

Findings

Critical exponents match those of regular cubic lattices.

Strong evidence for universality in critical behavior.

Finite-size scaling confirms theoretical predictions.

Abstract

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128,000 approx. 503 sites which are linked together according to the Voronoi/Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and \phi^4 field theory on three-dimensional regular cubic lattices.