Replica trick with real replicas: A way to build in thermodynamic homogeneity

Details Replica trick with real replicas: A way to build in thermodynamic homogeneity Replica trick with real replicas: A way to build in thermodynamic homogeneity

2004-07-23

arxiv.org/abs/cond-mat/0407615v1

Progr. Theor. Phys. Suppl. 157, 99 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, presented at SPDSA2004 Hayama (Japan), to appear in Progr. Theor. Phys

Scientific paper

10.1143/PTPS.157.99

We use real replicas to investigate stability of thermodynamic homogeneity of the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses. Within the replica trick with the replica symmetric ansatz we show that the averaged free energy at low temperatures is not thermodynamically homogeneous. The demand of minimization of the inhomogeneity of thermodynamic potentials leads in a natural way to the hierarchical solution of the Parisi type. Conditions for the global thermodynamic homogeneity are derived and evaluated for the SK and $p$-spin infinite range models.

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