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Quantum spins and random loops on the complete graph

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arxiv 1811.12834 v2 pith:R6SUIOE2 submitted 2018-11-30 math-ph math.MPmath.PR

Jakob E. Björnberg , Jürg Fröhlich , Daniel Ueltschi This is my paper · ORCID
classification math-phmath.MPmath.PR
keywords modelscompletegraphquantumaccompaniedanalysisassociatedaveraged
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We present a systematic analysis of quantum Heisenberg-, XY- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating function of expectations of powers of the averaged spin density. Various critical exponents are determined. Certain objects of the associated loop models are shown to have properties of Poisson--Dirichlet distributions.

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  1. Critical Parameters for Loop and Bernoulli Percolation

    math.PR 2019-08 conditional novelty 7.0 of 10

    Infinite loops in random loop models on bounded-degree graphs occur strictly later than infinite clusters in the associated Bernoulli percolation.

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