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On Equilibrium Dynamics of Spin-Glass Systems

A. Crisanti·L. Leuzzi
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Abstract

We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a thermodynamically stable solution. We then present an alternative formulation, based on the Crisanti, Hörner and Sommers [Z. für Physik {\bf 92}, 257 (1993)] dynamical solution of the spherical $p$-spin spin glass model, reproducing a stable static limit that coincides, in the case of a one step Replica Symmetry Breaking Ansatz, with the solution at the dynamic free energy threshold at which the relaxing system gets stuck off-equilibrium. We formally extend our analysis to any number of Replica Symmetry Breakings $R$. In the limit $R\to\infty$ both formulations lead to the Parisi anti-parabolic differential equation. This is the special case, though, where no dynamic blocking threshold occurs. The new formulation does not contain the additional order parameter $Δ$ of the Sompolinsky theory.

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A. Crisanti, L. Leuzzi. 2006-11-21. On Equilibrium Dynamics of Spin-Glass Systems. https://doi.org/10.1103/physrevb.75.144301

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