Dynamics in the Sherrington-Kirkpatrick Ising spin glass at and above T-g

A solution of Sherrington Kirkpatrick model for Ising spin glass with physically acceptable entropy

Finite-size critical scaling in Ising spin glasses in the mean-field regime.

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one...

Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model.

The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherring...

Small-correlation expansions for the inverse Ising problem

Abstract We present a systematic small-correlation expansion to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations; in addition, we show how to sum some usefu...

Mechanism for the failure of the Edwards hypothesis in the Sherrington-Kirkpatrick spin glass

The dynamics of the Sherrington-Kirkpatrick model at T=0 starting from random spin configurations is considered. The metastable states reached by such dynamics are atypical of such states as a whole, in that the probability density of site energies, p , is small at =0. Since virtually all metastable states have a much larger p 0 , this behavior demonstrates a qualitative failure of the Edwards ...