Beyond the Mean Field Approximation for Spin Glasses

Abstract

We study the d-dimensional random Ising model using a Bethe-Peierls approximation in the framework of the replica method. We take into account the correct interaction only inside replicated clusters of spins. Our ansatz is that the interaction of the borders of the clusters with the external world can be described via an effective interaction among replicas. The Bethe-Peierls model is mapped into a single Ising model with a random gaussian field, whose strength (related to the effective coupling between two replicas) is determined via a self-consistency equation. This allows us to obtain analytic estimates of the internal energy and of the critical temperature in d dimensions.

plane TeX file,19 pages. 3 figures may be requested to Paladin at axscaq.aquila.infn.it

References in corpus (3)

• Constrained annealing for spin glasses
• Bethe-Peierls Approximation for the 2D Random Ising Model
• Mean Field Solution of the Random Ising Model on the Dual Lattice

Cited by in corpus (5)

• Loop expansion around the Bethe-Peierls approximation for lattice models
• Mean Field Dynamical Exponents in Finite-Dimensional Ising Spin Glass
• Classical transverse Ising spin glass with short- range interaction beyond the mean field approximation
• Scheme of the replica symmetry breaking for short- ranged Ising spin glass within the Bethe- Peierls method
• Ising spin glass with arbitrary spin beyond the mean field theory