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2015 Large cycles in random permutations related to the Heisenberg model
Jakob Björnberg
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Electron. Commun. Probab. 20: 1-11 (2015). DOI: 10.1214/ECP.v20-4328

Abstract

We study the weighted version of the interchange process where a permutation receives weight $\theta^{\#\mathrm{cycles}}$. For $\theta=2$ this is Tóth's representation of the quantum Heisenberg ferromagnet on the complete graph. We prove, for $\theta>1$, that large cycles appear at "low temperature".

Citation

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Jakob Björnberg. "Large cycles in random permutations related to the Heisenberg model." Electron. Commun. Probab. 20 1 - 11, 2015. https://doi.org/10.1214/ECP.v20-4328

Information

Accepted: 27 July 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1325.60152
MathSciNet: MR3384113
Digital Object Identifier: 10.1214/ECP.v20-4328

Subjects:
Primary: 60K35
Secondary: 60B15

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