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Loop correlations in random wire models
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Benassi, Costanza and Ueltschi, Daniel (2020) Loop correlations in random wire models. Communications in Mathematical Physics, 374 . pp. 525-547. doi:10.1007/s00220-019-03474-9 ISSN 0010-3616.
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Official URL: http://dx.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: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Communications in Mathematical Physics | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0010-3616 | ||||||||
Official Date: | March 2020 | ||||||||
Dates: |
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Volume: | 374 | ||||||||
Page Range: | pp. 525-547 | ||||||||
DOI: | 10.1007/s00220-019-03474-9 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) |
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