Weak instability of frustated fermionic models

Abstract

We study the Almeida-Thouless instability of two fermionic models analogous to spin glasses that exhibit frustration and that were solved some time ago with a replica symmetric ansatz. In the first model (I) we consider only the anisotropic, Ising-like limit, while in the second model (II) we consider the isotropic, Heisenberg-like Hamiltonian. In both models the interactions are of the Sherrington-Kirkpatrick type and the spins are represented by bilinear combinations of fermionic fields. While model I is almost classical, exhibiting a negative entropy at low temperatures, we show in this paper that the eigenvalue lRS is positive at the critical temperature and becomes negative at a temperature below the transition point. Model II is more interesting because λRS is positive at the critical temperature TSG , vanishes at T1>TSG , and becomes positive again at T2>T1. Although the entropy remains positive all the way down to T50, it presents a break of monotonicity when λRS becomes negative, indicating a negative specific heat in part of the instability region T2>T>T1 . The two stability regions in the ordered phase for T>T2 and T1>T>TSG are characterized by the correct sign of the entropy and specific heat. This seems to indicate that replica symmetry stability is enhanced in frustrated fermionic spin models.