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We study numerically the non-equilibrium critical properties of the Isingmodel defined on direct products of graphs, obtained from factor graphs withoutphase transition (Tc = 0). On this class of product graphs, the Ising modelfeatures a finite temperature phase transition, and we find a pattern ofscaling behaviors analogous to the one known on regular lattices: Observablestake a scaling form in terms of a function L(t) of time, with the meaning of agrowing length inside which a coherent fractal structure, the critical state,is progressively formed. Computing universal quantities, such as the criticalexponents and the limiting fluctuation-dissipation ratio X_\infty, allows us tocomment on the possibility to extend universality concepts to the criticalbehavior on inhomogeneous substrates.

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