Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

Compressible Sherrington-Kirkpatrick spin-glass model

Abstract. We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressuretemperature phase diagram, and obtain expressions for the critical boundarie...

Some Rigorous Results on the Sherrington-Kirkpatrick Spin Glass Model

We prove that in the high temperature regime (T/J > 1) the deviation of the total free energy of the Sherrington-Kirkpatrick (S-K) spin glass model from the easily computed logAv(ZN({βJ})) converges in distribution, as ΛΓ-KX), to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.

On the Distribution of Overlaps in the Sherrington-kirkpatrick Spin Glass Model

|This expository paper describes some of the analytic tools developed recently by S. Ghirlanda and F. Guerra in the investigation of the distribution of overlaps in the Sherrington-Kirkpatrick spin glass model and of Parisi's ultrametricity. In particular, we introduce to this task a simpliied model on which the Gaussian analysis is made easier, and describe, under the essential tool of self-av...

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...

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