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On Equilibrium Dynamics of Spin-Glass Systems | | A. Crisanti
; L. Leuzzi
; | | Date: |
15 Jun 2006 | | Subject: | Disordered Systems and Neural Networks; Statistical Mechanics | | Abstract: | We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model, that owns different Replica Symmetry Breaking phases, we first show that in the static limit the Sompolinsky theory fails to reproduce the Parisi solution, even in the Parisi gauge, for any finite number $R$ of replica symmetry breaking steps. We then present an alternative formulation, based on the Crisanti, H"orner and Sommers [Z. f"ur Physik {f 92}, 257 (1993)] dynamical solution of the spherical $p$-spin spin glass model, reproducing for any $R$ the correct static limit. In the limit $R oinfty$ both formulations lead to the Parisi anti-parabolic differential equation. The new formulation does not contain the additional parameter $Delta$ of the Sompolinsky theory for the anomalous contribution to the response function since this is naturally included at each level of the hierarchy. In terms of the Sompolinsky function $Delta(x)$ this is equivalent to say that in the new formulation the Parisi gauge is automatically imposed at each level of the hierarchy. | | Source: | arXiv, cond-mat/0606425 | | Services: | Forum | Review | PDF | Favorites | |
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