Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-12-19
Phys. Rev. B71, 214403 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
REVTeX4, 22 pages, second extended version to be published in Phys. Rev. B
Scientific paper
10.1103/PhysRevB.71.214403
We use real replicas within the Thouless, Anderson and Palmer construction to investigate stability of solutions with respect to uniform scalings in the phase space of the Sherrington-Kirkpatrick model. We show that the demand of homogeneity of thermodynamic potentials leads in a natural way to a thermodynamically dependent ultrametric hierarchy of order parameters. The derived hierarchical mean-field equations appear equivalent to the discrete Parisi RSB scheme. The number of hierarchical levels in the construction is fixed by the global thermodynamic homogeneity expressed as generalized de Almeida Thouless conditions. A physical interpretation of a hierarchical structure of the order parameters is gained.
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