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Castellani, Tommaso; Cavagna, Andrea

Spin-Glass theory for pedestrians. (English) Zbl 1456.82490

J. Stat. Mech. Theory Exp. 2005, No. 5, Paper No. P05012, 53 p. (2005).
Summary: In these notes the main theoretical concepts and techniques in the field of mean-field spin glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is analysed (the \(p\)-spin spherical model) by using three different approaches: thermodynamics, covering pure states, overlaps, overlap distribution, replica symmetry breaking, and the static transition; dynamics, covering the generating functional method, generalized Langevin equation, equations for the correlation and the response, the mode coupling approximation, and the dynamical transition; and finally complexity, covering the mean-field (Thouless-Anderson-Palmer) free energy, metastable states, entropy crisis, threshold energy, and saddles. Particular attention has been paid to the mutual consistency of the results obtained from the different methods.

Cited in 69 Documents

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)

Keywords:

disordered systems (theory); cavity and replica method; spin glasses (theory); slow dynamics and ageing (theory)
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References:

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