Critical behavior of the 3D-Ising model on a poissonian random lattice

TL;DR

This study investigates the critical behavior of the 3D Ising model on a Poissonian random lattice using Monte Carlo simulations, finding it shares the same universality class as the pure 3D Ising model.

Contribution

It introduces a simulation of the 3D Ising model on Voronoi-Delaunay lattices with distance-dependent coupling, demonstrating universality class equivalence.

Findings

Critical exponents match those of the pure 3D Ising model.

The system belongs to the same universality class as the pure model.

Distance-dependent coupling does not alter universality class.

Abstract

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D-ferromagnetic Ising model on three dimensional Voronoi-Delaunay lattices. It is assumed that the coupling factor $J$ varies with the distance $r$ between the first neighbors as $J(r) \propto e^{-ar}$, with $a \ge 0$. The critical exponents $\gamma/\nu$, $\beta/\nu$, and $\nu$ are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.