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Charting the replica symmetric phase
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Coja-Oghlan, Amin, Efthymiou, Charilaos, Jaafari, Nor, Kang, Mihyun and Kapetanopoulos, Tobias (2018) Charting the replica symmetric phase. Communications in Mathematical Physics, 359 (2). pp. 603-698. doi:10.1007/s00220-018-3096-x
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Official URL: https://doi.org/10.1007/s00220-018-3096-x
Abstract
Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and computer science. In a path-breaking paper based on the non-rigorous ‘cavity method’, physicists predicted not only the existence of a replica symmetry breaking phase transition in such models but also sketched a detailed picture of the evolution of the Gibbs measure within the replica symmetric phase and its impact on important problems in combinatorics, computer science and physics (Krzakala et al. in Proc Natl Acad Sci 104:10318–10323, 2007). In this paper we rigorise this picture completely for a broad class of models, encompassing the Potts antiferromagnet on the random graph, the k-XORSAT model and the diluted k-spin model for even k. We also prove a conjecture about the detection problem in the stochastic block model that has received considerable attention (Decelle et al. in Phys Rev E 84:066106, 2011).
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QC Physics | |||||||||||||||
| Divisions: | Faculty of Science > Computer Science Faculty of Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Phase transformations (Statistical physics), Statistical mechanics | |||||||||||||||
| Journal or Publication Title: | Communications in Mathematical Physics | |||||||||||||||
| Publisher: | Springer Berlin Heidelberg | |||||||||||||||
| ISSN: | 0010-3616 | |||||||||||||||
| Official Date: | April 2018 | |||||||||||||||
| Dates: |
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| Volume: | 359 | |||||||||||||||
| Number: | 2 | |||||||||||||||
| Page Range: | pp. 603-698 | |||||||||||||||
| DOI: | 10.1007/s00220-018-3096-x | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| RIOXX Funder/Project Grant: |
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