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Thermodynamic origin of order parameters in mean‐field models of spin glasses
Author(s) -
Janiš V.,
Zdeborová L.
Publication year - 2006
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200541070
Subject(s) - spin glass , order (exchange) , field (mathematics) , statistical physics , spin (aerodynamics) , physics , condensed matter physics , mathematics , thermodynamics , business , finance , pure mathematics
We analyze the thermodynamic behavior of general n ‐component mean‐field spin glass models in order to identify the origin of the hierarchical structure of the order parameters from the replica‐symmetry breaking solution. We derive a configurationally dependent free energy with local magnetizations and averaged local susceptibilities as order parameters. Using an example of the replicated Ising spin glass we demonstrate that the hierarchy of order parameters in mean‐field models results from the structure of inter‐replica susceptibilities. These susceptibilities serve for lifting the degeneracy due to the existence of many metastable states and for recovering the thermodynamic homogeneity of the free energy. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)