Replica Plefka expansion of Ising systems

Muneki Yasuda, Yoshiyuki Kabashima, Kazuyuki Tanaka

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The replica extension theory has been developed for the purpose of investigating spin glass systems in the replica symmetry breaking phase. The replica extension theory is a replica theory for a specific sample and has the scheme of the one-step replica symmetry breaking ansatz. In this paper, using the Plefka expansion, we propose the perturbative expansion of Gibbs free energies of Ising systems with the replica extension theory, and we derive the explicit form of the second-and third-order approximations. Our Plefka expansion systematically provides perturbative approximations taking the one-step replica symmetry breaking into account. In some numerical experiments, we show that our perturbative approximations are quantitatively superior to conventional perturbative approximations that do not take the one-step replica symmetry breaking into account in the spin glass phase.

Original languageEnglish
Article numberP04002
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number4
Publication statusPublished - 2012 Apr


  • cavity and replica method
  • message-passing algorithms
  • spin glasses (theory)
  • statistical inference

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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