Two-dimensional Ising model on random lattices with constant coordination number

TL;DR

This study investigates the critical behavior of the 2D Ising model on random lattices with fixed coordination number, revealing disorder-dependent critical exponents and emphasizing the importance of lattice topology on phase transition stability.

Contribution

It introduces a novel type of quenched topological disorder in the 2D Ising model and analyzes its effects on critical exponents through large-scale Monte Carlo simulations.

Findings

Disorder-dependent effective critical exponents observed

No clear universal behavior found across different lattices

Lattice planarity and connectedness influence phase transition stability

Abstract

We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta (2014), our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.