On one-step replica symmetry breaking in the Edwards-Anderson spin glass model

• Published in: Journal of statistical mechanics 2016-07, Vol.2016 (7), p.73305
• Main Authors: Ferraro, Gino Del, Wang, Chuang, Zhou, Hai-Jun, Aurell, Erik
• Format: Article
• Language: English
• Subjects: Fysik; generalized belief propagation; generalized survey propagation; low temperature; Physics; Region graph approximations; survey propagation
• ISSN: 1742-5468; 1572-9613; 0022-4715; 1742-5468
• DOI: 10.1088/1742-5468/2016/07/073305

We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a generalized belief propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter y, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to the Bethe approximation case for tree-like graphs, where it has been shown that 1RSB belief propagation equations admit a survey propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of generalized survey propagation equations for the single instance graph case.