Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-09-14
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages, 2 figures
Scientific paper
The spin glass behavior near zero temperature is a complicated matter. To get an easier access to the spin glass order parameter $Q(x)$ and, at the same time, keep track of $Q_{ab}$, its matrix aspect, and hence of the Hessian controlling stability, we investigate an expansion of the replicated free energy functional around its ``spherical'' approximation. This expansion is obtained by introducing a constraint-field and a (double) Legendre Transform expressed in terms of spin correlators and constraint-field correlators. The spherical approximation has the spin fluctuations treated with a global constraint and the expansion of the Legendre Transformed functional brings them closer and closer to the Ising local constraint. In this paper we examine the first contribution of the systematic corrections to the spherical starting point.
Crisanti Andrea
Dominicis Cirano de
Sarlat Thomas
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