Non-equilibrium critical properties of the Ising model on product graphs

TL;DR

This study investigates the non-equilibrium critical behavior of the Ising model on product graphs, revealing scaling laws and universal quantities that suggest extending universality concepts to inhomogeneous substrates.

Contribution

It introduces a numerical analysis of the Ising model on product graphs, demonstrating critical scaling and universality in inhomogeneous structures.

Findings

Scaling behavior analogous to regular lattices

Universal critical exponents identified

Finite limiting fluctuation-dissipation ratio X_∞

Abstract

We study numerically the non-equilibrium critical properties of the Ising model defined on direct products of graphs, obtained from factor graphs without phase transition (Tc = 0). On this class of product graphs, the Ising model features a finite temperature phase transition, and we find a pattern of scaling behaviors analogous to the one known on regular lattices: Observables take a scaling form in terms of a function L(t) of time, with the meaning of a growing length inside which a coherent fractal structure, the critical state, is progressively formed. Computing universal quantities, such as the critical exponents and the limiting fluctuation-dissipation ratio X_\infty, allows us to comment on the possibility to extend universality concepts to the critical behavior on inhomogeneous substrates.