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We use real replicas within the Thouless, Anderson and Palmer construction toinvestigate stability of solutions with respect to uniform scalings in thephase space of the Sherrington-Kirkpatrick model. We show that the demand ofhomogeneity of thermodynamic potentials leads in a natural way to athermodynamically dependent ultrametric hierarchy of order parameters. Thederived hierarchical mean-field equations appear equivalent to the discreteParisi RSB scheme. The number of hierarchical levels in the construction isfixed by the global thermodynamic homogeneity expressed as generalized deAlmeida Thouless conditions. A physical interpretation of a hierarchicalstructure of the order parameters is gained.Comment: REVTeX4, 22 pages, second extended version to be published in Phys.  Rev.

Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space