Replica Symmetry Breaking in Short Range Spin Glasses: A Review of the Theoretical Foundations and of the Numerical Evidence

Details Replica Symmetry Breaking in Short Range Spin Glasses: A Review of the Theoretical Foundations and of the Numerical Evidence Replica Symmetry Breaking in Short Range Spin Glasses: A Review of the Theoretical Foundations and of the Numerical Evidence

1999-06-05

arxiv.org/abs/cond-mat/9906076v1

J.Statist.Phys. 98 (2000) 973

Physics

Condensed Matter

Disordered Systems and Neural Networks

46 pages with 21 ps figures included

Scientific paper

We discuss Replica Symmetry Breaking (RSB) in Spin Glasses. We present an update about the state of the matter, both from the analytical and from the numerical point of view. We put a particular attention in discussing the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss about what happens in finite dimensional, realistic spin glasses. Together with a detailed review of some of most important features, facts, data, phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field and the dynamical approach. We present new numerical results for the behavior of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example the determination of the phase transition point, the correlation functions, the window overlaps, the dynamical behavior of the system).

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