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Probabilistic representation of quantum correlation

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We consider lattice models of quantum spins that can be represented by random loop models in one more dimensions. Such models have been introduced over the years by Ginibre, Conlon-Solovej, Toth, and Aizenman-Nachtergaele. Long-range correlations are given by loops of macroscopic lengths. We argue that their joint distribution is given by the Poisson-Dirichlet distribution for random partitions. I will review some results that support this conjecture, results that come from either rigorous statistical mechanics, or from probability theory. This is joint work with C. Goldschmidt and P. Windridge.

This talk is part of the Probability series.

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