Classical transverse Ising spin glass with short- range interaction beyond the mean field approximation

TL;DR

This paper investigates the classical transverse Ising spin glass with short-range interactions beyond mean-field theory, deriving critical properties and phase diagrams for various dimensions using a modified Bethe-Peierls approach.

Contribution

It introduces a modified Bethe-Peierls method to analyze short-range transverse Ising spin glasses beyond mean-field approximation for different dimensions.

Findings

Analytical expressions for critical transverse field and susceptibility at zero temperature.

Numerical phase diagrams for various dimensions.

Consistency with mean-field results as dimension approaches infinity.

Abstract

The classical transverse field Ising spin- glass model with short-range interactions is investigated beyond the mean- field approximation for a real d- dimensional lattice. We use an appropriate nontrivial modification of the Bethe- Peierls method recently formulated for the Ising spin- glass. The zero- temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d. The phase diagram is also calculated numerically for different values of d. In the limit d -> infinity, known mean- field results are consistently reproduced.