Many-Body Physics: From Kondo to Hubbard

0456231 - FZÚ 2016 RIV DE eng M - Monography Chapter
Janiš, Václav
Introduction to mean-field theory of spin glass models.
Many-Body Physics: From Kondo to Hubbard. Jülich: Forschungszentrums Jülich, 2015 - (Pavarini, E.; Koch, E.; Coleman, P.), s. 8.1-8.28. ISBN 978-3-95806-074-6
Institutional support: RVO:68378271
Keywords : mean-field theory * spin-glass models * ergodicity breaking * real replicas * asymptotic expansions
Subject RIV: BM - Solid Matter Physics ; Magnetism
http://www.cond-mat.de/events/correl15/manuscripts/janis.pdf

We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry breaking to ergodicity breaking and use the concept of real replicas to restore thermodynamic homogeneity of the equilibrium free energy in a replicated phase space. Embedded replications of the spin variables result in a set of hierarchical free energies and overlap susceptibilities between replica hierarchies as order parameters. The limit to infinite number of replica hierarchies leads to the Parisi solution with a continuous replica-symmetry breaking. We demonstrate the construction of the spin-glass mean-field solutions via real replicas on three spin-glass models: Ising, Potts and p-spin. An asymptotic expansion in each model is used to demonstrate various types of the transition from the paramagnetic to the glassy phase.
Permanent Link: http://hdl.handle.net/11104/0256789