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

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

2010-12-17

arxiv.org/abs/1012.3852v1

J. Stat. Mech. (2010) P12024

Physics

Condensed Matter

Statistical Mechanics

11 pages, 7 figures

Scientific paper

10.1088/1742-5468/2010/12/P12024

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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