J. Phys. I France
Volume 5, Numéro 7, July 1995
Page(s) 805 - 813
DOI: 10.1051/jp1:1995164
J. Phys. I France 5 (1995) 805-813

Thouless-Anderson-Palmer Approach to the Spherical p-Spin Spin Glass Model

A. Crisanti1 and H.-J. Sommers2

1  Dipartimento di Fisica, Università "La Sapienza", 00185 Roma, Italy
2  Fachbereich Physik, Universität-Gesamthochschule Essen, 45141 Essen, Germany

(Received 20 February 1995, accepted 27 March 1995)

We analyze the Thouless-Anderson-Palmer (TAP) approach to the spherical p-spin spin glass model in zero external field. The TAP free energy is derived by summing up all the relevant diagrams for $N\to \infty$ of a diagrammatic expansion of the free energy. We find that if the multiplicity of the TAP solutions is taken into account, there is a first order transition in the order parameter at the critical temperature $T_{\rm c}$ higher than that predicted by the replica solution $T_{\rm RSB}$, but in agreement with the results of dynamics. The transition is of "geometrical" nature since the new state has larger free energy but occupies the largest volume in phase space. The transition predicted by the replica calculation is also of "geometrical" nature since it corresponds to the states with smallest free energy with positive complexity.

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