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

Abstract

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