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Universal behaviour of 3D loop soup models
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Ueltschi, Daniel (2017) Universal behaviour of 3D loop soup models. In: 6th Warsaw School of Statistical Physics, Sandomierz, Poland, 25 Jun - 2 Jul 2016. Published in: Proceedings of 6th Warsaw School of Statistical Physics pp. 65-100.
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Official URL: http://www.worldcat.org/oclc/1014076186
Abstract
These notes describe several loop soup models and their {\it universal behaviour} in dimensions greater or equal to 3. These loop models represent certain classical or quantum statistical mechanical systems. These systems undergo phase transitions that are characterised by changes in the structures of the loops. Namely, long-range order is equivalent to the occurrence of macroscopic loops. There are many such loops, and the joint distribution of their lengths is always given by a {\it Poisson-Dirichlet distribution}.
This distribution concerns random partitions and it is not widely known in statistical physics. We introduce it explicitly, and we explain that it is the invariant measure of a mean-field split-merge process. It is relevant to spatial models because the macroscopic loops are so intertwined that they behave effectively in mean-field fashion. This heuristics can be made exact and it allows to calculate the parameter of the Poisson-Dirichlet distribution. We discuss consequences about symmetry breaking in certain quantum spin systems.
Item Type: | Conference Item (Paper) | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Proceedings of 6th Warsaw School of Statistical Physics | ||||||
Publisher: | Warsaw University Press | ||||||
Editor: | Cichocki, B. and Napiorkowski, M. and Piasecki, J. and Szymcza, P. | ||||||
Official Date: | 2017 | ||||||
Dates: |
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Page Range: | pp. 65-100 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 17 May 2018 | ||||||
Conference Paper Type: | Paper | ||||||
Title of Event: | 6th Warsaw School of Statistical Physics | ||||||
Type of Event: | Conference | ||||||
Location of Event: | Sandomierz, Poland | ||||||
Date(s) of Event: | 25 Jun - 2 Jul 2016 | ||||||
Related URLs: | |||||||
Open Access Version: |
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