Loop Correlations in Random Wire Models

Benassi, Costanza and Ueltschi, Daniel (2020) Loop Correlations in Random Wire Models. Communications in Mathematical Physics, 374 (2). pp. 525-547. ISSN 0010-3616

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Official URL: https://doi.org/10.1007/s00220-019-03474-9

Abstract

We introduce a family of loop soup models on the hypercubic lattice. The models involve links on the edges, and random pairings of the link endpoints on the sites. We conjecture that loop correlations of distant points are given by Poisson-Dirichlet correlations in dimensions three and higher. We prove that, in a specific random wire model that is related to the classical XY spin system, the probability that distant sites form an even partition is given by the Poisson-Dirichlet counterpart.

Item Type: Article
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Paul Burns
Date Deposited: 15 May 2019 13:29
Last Modified: 08 Jun 2020 08:01
URI: http://nrl.northumbria.ac.uk/id/eprint/39320

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