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Phase transition for loop representations of Quantum spin systems on trees

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arxiv 1804.00860 v1 pith:R2TYWGEU submitted 2018-04-03 math-ph math.MP

Volker Betz , Johannes Ehlert , Benjamin Lees This is my paper · ORCID
classification math-phmath.MP
keywords loopsdistributiongalton-watsonoffspringphasequantumspinsystems
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abstract

We consider a model of random loops on Galton-Watson trees with an offspring distribution with high expectation. We give the configurations a weighting of $\theta^{\#\text{loops}}$. For many $\theta>1$ these models are equivalent to certain quantum spin systems for various choices of the system parameters. We find conditions on the offspring distribution that guarantee the occurrence of a phase transition from finite to infinite loops for the Galton-Watson tree.

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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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