Charting the replica symmetric phase
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.: PNAS 2007]. In this paper we rigorise this picture completely for a broad class of models, encompassing the Potts antiferromagnet on the random graph, the -XORSAT model and the diluted -spin model for even . We also prove a conjecture about the detection problem in the stochastic block model that has received considerable attention [Decelle et al.: Phys. Rev. E 2011].
Keywords
Cite
@article{arxiv.1704.01043,
title = {Charting the replica symmetric phase},
author = {Amin Coja-Oghlan and Charilaos Efthymiou and Nor Jaafari and Mihyun Kang and Tobias Kapetanopoulos},
journal= {arXiv preprint arXiv:1704.01043},
year = {2018}
}