Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field

Abstract

The stability of spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field $\Gamma$. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues ${\lambda }_{\pm }$ of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when $\Gamma$ is increased. Therefore, this result suggests that the study of the replicon can not be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the ${\lambda }_{\pm }$ indicate instability problems for the SG solution close to all range of first order boundary.

arXiv comment15 pages, 4 figures, accepted in Physica A

References in corpus (15)

• Quantum phase transition in spin glasses with multi-spin interactions
• Spin Glass and ferromagnetism in disordered Cerium compounds
• First Order Phase Transition and Phase Coexistence in a Spin-Glass Model
• The Ising spin glass in a transverse field. Results of two fermionic models
• Role of the transverse field in inverse freezing in the fermionic Ising spin-glass model
• Replica symmetry breaking solution for the fermionic Ising spin glass and the Ghatak-Sherrington model
• Quantum critical point in the spin glass-antiferromagnetism competition in Kondo-lattice systems
• Tricritical behaviour of Ising spin glasses with charge fluctuations
• Quantum critical point in the spin glass-antiferromagnetism competition for fermionic Ising Models
• On exact mappings between fermionic Ising spin glass and classical spin glass models
• Parisi-Symmetry of the Many-Body Quantum Theory of randomly interacting fermionic systems
• One-step replica symmetry breaking solution for fermionic Ising spin glass in a transverse field
• Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field
• Replica symmetry breaking in the transverse-field Ising spin-glass model: Two frmionic representations
• Stability of a two-sublattice spin-glass model

Cited by in corpus (1)

• Fermionic van Hemmen Spin Glass Model with a Transverse Field