On the Tail of the Overlap Probability Distribution in the Sherrington--Kirkpatrick Model

Abstract

We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here generically $\frac{1}{N}\log P_N(q)$ $\approx$ $-\mathcal{A}$ $((|q|-q_{EA}{)}^3$, and we compute the first correction to the expansion of $\A$ in powers of $T_c-T$. We study also the $q=1$ case, where $P(q)$ is know exactly. Finally we study the paramagnetic phase, where exact results valid for all $q$'s are obtained. The overall agreement between the various points of view is very satisfactory. Data from large scale numerical simulations show that the predicted behavior can be detected already on moderate lattice sizes.

18 pages including ps figures

References in corpus (3)

• Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
• Correlation Time Scales in the Sherrington-Kirkpatrick Model
• About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass

Cited by in corpus (8)

• Finite size corrections in the Sherrington-Kirkpatrick model
• Clustering analysis of the ground-state structure of the vertex-cover problem
• Magnetic field chaos in the SK Model
• On the structure of correlations in the three dimensional spin glasses
• Bond chaos in the Sherrington-Kirkpatrick model
• A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model
• Solution-space structure of (some) optimization problems
• Pair correlation function for spin glasses