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arXiv · 1012.3852

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

R. Burioni·F. Corberi·A. Vezzani
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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.

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R. Burioni, F. Corberi, A. Vezzani. 2010-12-17. Non-equilibrium critical properties of the Ising model on product graphs. https://doi.org/10.1088/1742-5468%2F2010%2F12%2Fp12024

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