Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model

Details Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model

2001-11-02

arxiv.org/abs/cond-mat/0111037v5

Phys. Rev. E 65, 046137 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 11 figures, RevTeX 4.0

Scientific paper

10.1103/PhysRevE.65.046137

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from the numerical solution of the infinity-replica symmetry breaking equations which are solved using a new pseudo-spectral code which allows for very accurate results. With this methods we are able to get more insight into the analytical properties of the solutions. We are also able to determine numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T --> 0} x_{max}(T) > 0.5.

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