Metastates in mean-field models with random external fields generated by Markov chains

Details Metastates in mean-field models with random external fields generated by Markov chains Metastates in mean-field models with random external fields generated by Markov chains

2011-09-20

arxiv.org/abs/1109.4246v2

Physics

Mathematical Physics

20 pages, 2 figures

Scientific paper

We extend the construction by Kuelske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that, for a degenerate non-reversible chain this CLT approximation is not enough and the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.

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