Fermionic TAP-equations

TL;DR

This paper derives and analyzes the TAP equations for the fermionic Ising spin glass, identifying phase transitions, stability conditions, and complex solution structures at zero temperature.

Contribution

It introduces the fermionic TAP equations, explores their stability, and uncovers a first order phase transition at zero temperature.

Findings

Identified the breakdown of the paramagnetic phase.

Localized a first order transition at μ ≈ 0.8.

Computed the filling factor and internal field distribution at T=0.

Abstract

We derive the TAP equations for the fermionic Ising spin glass. It is found that, just as in the non-fermionic model, the conditions for stability and for validity of the free energy are equivalent. We determine the breakdown of the paramagnetic phase. Numeric solutions of the fermionic TAP-equations at T=0 allowed to localize a first order transition between the spin glass phase and the paramagnetic phase at $\mu \approx 0.8$. We computed at zero temperature the filling factor $\nu(\mu)$ and the distribution of internal fields. The saddle-point equations resulting from the calculation of the number of solutions to the TAP-equations were found to be much more complicated as in the non-fermionic case.