Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Phase Diagram of a Quantum Hopfield Spin Glass with the Pseudo-Inverse Rule

Yu‐qiang Ma, Chang-De Gong

Published Apr 30, 1995• 0 citations
Publisher

Abstract

A quantum Ising spin-glass model in a transverse field is presented. The network is based on a modified version of the Hopfield spin glass. The equations for the order parameters describing the ordered phases are obtained, and the phase transitions of the system are analyzed. The ordered phases are suppressed by the existence of both quantum effects and the random overlaps between the patterns.

DOI
10.1088/0253-6102/23/3/303

Related papers

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

Yu‐qiang Ma, Chang-De Gong

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.

Physical review. B, Condensed matter•Sep 1, 1994•0 citations

Hopfield spin-glass model in a transverse field

Yu‐qiang Ma, Chang-De Gong

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.

Physical review. B, Condensed matter•Nov 1, 1993•12 citations

Statistical mechanics of a Hopfield neural-network model in a transverse field

Yu‐qiang Ma, Yueming Zhang, Y. G. +1 more

We construct a soluble model to describe the retrieval properties of the quantum transverse Hopfield model in neural networks. A set of equations for the order parameters describing retrieval and spin-glass phases of the Hopfield model in a transverse field are obtained. Based on these equations, phase diagrams are examined and the memory storage capacity of the networks is analyzed as a function of the temperature and transverse field.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jun 1, 1993•10 citations

Quantum transverse Ising spin-glass model in the mean-field approximation

Katarzyna Walasek, K. Lukierska‐Walasek

A mean-field approximation is used to investigate the quantum transverse Ising spin-glass model in the Edwards-Anderson version. We introduce two order parameters, diagonal and off diagonal in replica indices, and discuss their physical significance. The effective free-energy function is obtained, and the critical value of the transverse field $\ensuremath{\Gamma}$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\ensuremath{\Gamma}$,$T$ plane is also given.

Physical review. B, Condensed matter•Oct 1, 1986•32 citations

Phase diagram for the infinite-range transverse Ising spin-glass model

Terufumi Yokota

We obtain the phase diagram for the infinite-range transverse Ising spin-glass model by the pair approximation. The transition temperature increases slightly for small transverse field \ensuremath{\Gamma} because the quantum fluctuation suppresses the reaction field. For \ensuremath{\Gamma}/J\ifmmode \tilde{}\else \~{}\fi{}>1+\ensuremath{\surd}3/8, the system is always paramagnetic.

Physical review. B, Condensed matter•Nov 1, 1989•16 citations

Soluble model to treat the quantum spin glass

J. Roberto Viana, Yamilles Nogueira, J. Ricardo de Sousa

The van Hemmen model with a transverse field is studied to describe the quantum Ising spin glass. The free energy and phase diagrams $(T$ versus $\ensuremath{\Omega},$ and T versus ${J}_{o}/J,$ where $\ensuremath{\Omega}$ is the transverse field, ${J}_{o}$ and J are the ferromagnetic and random exchange interactions, respectively) are calculated for the model with two-peaked and Gaussian exchange distribution. The system presents three ordered phases, namely, spin glass, mixed, and ferromagnetic phases, besides the paramagnetic disordered phase. The influence of the transverse field $\ensuremath{\Omega}$ is to destroy the ordered phases. In the $(T,\ensuremath{\Omega})$ plane our results are compared with those obtained by the replica-symmetry-breaking solution and the same qualitative behavior is observed for the spin-glass transition.

Physical review. B, Condensed matter•Sep 19, 2002•8 citations
A quantum Ising spin-glass model in a transverse field is presented. The network is based on a modified version of the Hopfield spin glass. The equations for the order parameters describing the ordered phases are obtained, and the phase transitions of the system are analyzed. The ordered phases are suppressed by the existence of both quantum effects and the random overlaps between the patterns.
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.
A mean-field approximation is used to investigate the quantum transverse Ising spin-glass model in the Edwards-Anderson version. We introduce two order parameters, diagonal and off diagonal in replica indices, and discuss their physical significance. The effective free-energy function is obtained, and the critical value of the transverse field $\ensuremath{\Gamma}$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\ensuremath{\Gamma}$,TTT plane is also given.
The van Hemmen model with a transverse field is studied to describe the quantum Ising spin glass. The free energy and phase diagrams (T(T(T versus $\ensuremath{\Omega},$ and T versus Jo/J,{J}_{o}/J,Jo​/J, where $\ensuremath{\Omega}$ is the transverse field, Jo{J}_{o}Jo​ and J are the ferromagnetic and random exchange interactions, respectively) are calculated for the model with two-peaked and Gaussian exchange distribution. The system presents three ordered phases, namely, spin glass, mixed, and ferromagnetic phases, besides the paramagnetic disordered phase. The influence of the transverse field $\ensuremath{\Omega}$ is to destroy the ordered phases. In the $(T,\ensuremath{\Omega})$ plane our results are compared with those obtained by the replica-symmetry-breaking solution and the same qualitative behavior is observed for the spin-glass transition.