Electronic Communications in Probability

Large cycles in random permutations related to the Heisenberg model

Jakob Björnberg

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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".

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 55, 11 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320982

Digital Object Identifier
doi:10.1214/ECP.v20-4328

Mathematical Reviews number (MathSciNet)
MR3384113

Zentralblatt MATH identifier
1325.60152

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

Keywords
Interchange process Heisenberg model

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Björnberg, Jakob. Large cycles in random permutations related to the Heisenberg model. Electron. Commun. Probab. 20 (2015), paper no. 55, 11 pp. doi:10.1214/ECP.v20-4328. https://projecteuclid.org/euclid.ecp/1465320982


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References

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