Complexity in mean-field spin-glass models: Ising p-spin
- Dipartimento di Fisica, SMC and INFM, Universita di Roma 'La Sapienza', Piazzalele Aldo. Moro 2, I-00185 Rome (Italy)
The complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising p-spin is investigated in the temperature regime where the equilibrium phase is one-step replica symmetry breaking. Two solutions of the resulting saddle point equations are found. One is supersymmetric (SUSY) and includes the equilibrium value of the free energy while the other is non-SUSY. The two solutions cross exactly at a value of the free energy where the replicon eigenvalue is zero; at low free energy the complexity is described by the SUSY solution while at high free energy it is described by the non-SUSY solution, the latter accounting for the total number of solutions. The relevant TAP solutions counted by the non-SUSY complexity share the same features of the corresponding solutions in the Sherrington-Kirkpatrick model; in particular their Hessian has a vanishing isolated eigenvalue. The TAP solutions corresponding to the SUSY complexity, instead, are well separated minima.
- OSTI ID:
- 20666288
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 71, Issue 9; Other Information: DOI: 10.1103/PhysRevB.71.094202; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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