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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

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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
Subjects: Q Science > QC Physics
Divisions: Faculty of Science > Computer Science
Faculty of Science > Mathematics
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:
DateEvent
April 2018Published
1 February 2018Available
15 December 2017Accepted
Date of first compliant deposit: 20 March 2019
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:
Project/Grant IDRIOXX Funder NameFunder ID
278857–PTCCSeventh Framework Programmehttp://dx.doi.org/10.13039/100011102
EF 103/1-1[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
P26826Austrian Science Fundhttp://dx.doi.org/10.13039/501100002428
UNSPECIFIEDStiftung Polytechnische GesellschaftUNSPECIFIED

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