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Physical review. B, Condensed matter

Reentrant phase transition in the quantum-spin-glass model with the pseudoinverse rule

Yu‐qiang Ma, Chang-De Gong

Published Sep 1, 1994• 0 citations
Publisher

Abstract

We examine a quantum-spin-glass model with a transverse field. The network is based on a modified version of the Hopfield spin glass. A set of equations for the order parameters describing the ordered phases are obtained, and the effects of the quantum fluctuations and the stored patterns on the phase transitions between the ordered phases are examined. We see that reentry occurring in the mixed-phase transitions can be observed in the present system.

DOI
10.1103/physrevb.50.7165

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•Oct 31, 2006•0 citations
We examine a quantum-spin-glass model with a transverse field. The network is based on a modified version of the Hopfield spin glass. A set of equations for the order parameters describing the ordered phases are obtained, and the effects of the quantum fluctuations and the stored patterns on the phase transitions between the ordered phases are examined. We see that reentry occurring in the mixed-phase transitions can be observed in the present system.
A quantum Hopfield spin-glass model with transverse fields is presented. A set of equations for the order parameters of a large class of spin-glass models with transverse fields is obtained, and the phase transitions are analyzed with a finite number of patterns p. We find that a reentrant phenomenon is possible for a quantum Mattis model with transverse fields, contrary to the quantum transverse Sherrington-Kirkpatrick-like model. The effects of quantum fluctuations (induced by the transverse field) on the ordered phases of systems with competing interactions are also discussed.
The phase diagram of the spin 1 quantum van Hemmen spin glass model with biaxial crystal-field anisotropy and a transverse magnetic field is studied. We investigate the effects of the two transverse crystal-field parameters (Dx{D}_{x}Dx​ and Dy{D}_{y}Dy​) and transverse field $(\ensuremath{\Omega})$ on the phase diagrams in the $T\ensuremath{-}{D}_{x}$ plane for various values of Dy{D}_{y}Dy​ and $\ensuremath{\Omega}$. Tricritical and reentrant behavior can be seen for appropriate ranges of these parameters.
The present work analyzes the fermionic Ising spin glass model in a transverse magnetic field. The problem is written in the Grand Canonical ensemble with the spin operators represented by bilinear combinations of fermionic fields. The transverse field is a spin "flip" mechanism and inserts quantum fluctuations, which can lead the transition temperature Tj to quantum critical point (QCP). In this case, the phase transition from spin glass to paramagnetic phases occurs in T = o. On the other hand, charge fluctuations controlled by chemical potentiall-L show the existence of a tricritical point. The replica method with replica symmetry and static approximation are used to solve this problem. However, the replica symmetry solution shows some problems, like negative entropy in low temperatures. Thus, the stability conditions are derived to test the generated solution of this IDodel. The main purpose of this work is to study the competition between spin glass and paramagnetic phases with both quantum and charge fluctuations. After the stability conditions are derived, a detailed sight into the generated solution is shown under the form of diagrams phase. The stability conditions, however, show another applications in the present problem, once they can be used, for instance, in the tricritical point derivation.