Replica symmetry breaking solution for the fermionic Ising spin glass and the Ghatak-Sherrington model

TL;DR

This paper provides an exact solution for the fermionic Ising spin glass with replica symmetry breaking, offering new insights into phase transitions and stability analysis, and extends the solution to the S=1 Ghatak-Sherrington model.

Contribution

It introduces a novel solution method for the fermionic Ising spin glass with replica symmetry breaking and maps it to the S=1 Ghatak-Sherrington model, improving understanding of phase transitions.

Findings

Derived an analytic expression for T=0 critical point.

Found that complex eigenvalues indicate instability beyond replica symmetry.

Mapped fermionic spin glass to the S=1 Ghatak-Sherrington model.

Abstract

We solve the fermionic version of the Ising spin glass for arbitrary filling \mu and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from \mu to the anisotropy parameter D, we also obtain the solution of the S=1 Sherrington-Kirkpatrick model. An analytic expression for T=0 gives an improved critical value for the first-order phase transition. We revisit the question of stability against replica-diagonal fluctuations and find that the appearance of complex eigenvalues of the Almeida-Thouless matrix is not an artifact of the replica-symmetric approximation.