On the TAP approach to the spherical p-spin SG model

A. Crisanti; H. -J. Sommers

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arXiv · cond-mat/9406051

On the TAP approach to the spherical p-spin SG model

A. Crisanti·H. -J. Sommers

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Abstract

In this letter we analyze the 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, then 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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A. Crisanti, H. -J. Sommers. 1994-06-13. On the TAP approach to the spherical p-spin SG model. https://arxiv.org/abs/cond-mat/9406051

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