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

Phase diagram of the random energy model with ferromagnetic bias in the presence of a transverse field

Tomoyuki Obuchi, Hidetoshi Nishimori

Published Nov 7, 2006• 0 citations
OpenAlex

Abstract

The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p \to \infty$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit $p \to \infty$ by using the large-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.

Related papers

Phase Diagram of the p-Spin-Interacting Spin Glass with Ferromagnetic Bias and a Transverse Field in the Infinite- p Limit

Tomoyuki Obuchi, Hidetoshi Nishimori, David Sherrington

The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p \to \infty$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit $p \to \infty$ by using the large-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.

arXiv:cond-mat/0611168•Journal of the Physical Society of Japan•May 11, 2007•22 citations

Solvable model of the quantum spin glass in a transverse field

Yadin Y. Goldschmidt

The spin-glass model with p-spin interactions in the presence of a transverse field is solved in the limit p\ensuremath{\rightarrow}\ensuremath{\infty}. The phase diagram is obtained and consists of three phases: A spin-glass phase and two paramagnetic phases. The paramagnetic phases are distinguished by transverse ordering. The spin-glass phase is similar to that of the random-energy model.

Physical review. B, Condensed matter•Mar 1, 1990•110 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

Infinite-range Ising spin glass in a transverse field

Dave Thirumalai, Qiang Li, T. R. Kirkpatrick

The infinite-range Ising spin glass in the presence of a transverse field is considered. Using the generalised Trotter formula and replica methods, the free energy for the system with quenched random bond interactions is evaluated using the static approximation. It is shown that, when the strength of the transverse field equals the largest eigenvalue of the random bond interaction matrix, the spin glass transition is destroyed. The authors also show that a replica-symmetric spin glass phase is stable in a certain region of the temperature-field phase diagram. Finally they present suggestive arguments which indicate that, when the time dependence of the dynamic susceptibility is included, then the stability of the replica-symmetric phase is enhanced.

Journal of Physics A Mathematical and General•Aug 21, 1989•81 citations

Large-Sanalysis of one-dimensional quantum-spin models in a transverse magnetic field

Diptiman Sen, Bikas K. Chakrabarti

We analyze the zero-temperature phase diagram of two kinds of one-dimensional quantum-spin models in a transverse magnetic field. The first kind has uniform nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic couplings. A spin-wave analysis indicates the presence of several (possibly an infinite number of) commensurate modulated phases in the phase diagram. The three most prominent phases are paramagnetic, ferromagnetic, and a q=(1/4 phase of period four. The second kind of model is a spin-glass with only nearest-neighbor ferromagnetic interactions whose strengths are random and are characterized by a probability function. A classical large-S analysis shows the existence of a Griffiths phase lying in between a low-magnetic-field ferromagnetic phase and a high-magnetic-field paramagnetic phase. We present two order parameters that can together distinguish between the three phases.

Physical review. B, Condensed matter•Mar 1, 1990•7 citations

1/p expansion for a p-spin interaction spin-glass model in a transverse field

V. Dobrosavljević, Dave Thirumalai

The authors develop systematic 1/ rho expansions for the rho -spin interaction spin-glass model in a transverse field. This model can be solved using the static approximation (SA), which is expected to be valid in the limit rho to infinity . For large, but finite rho , corrections to SA can be obtained, and the non-trivial time dependence of the imaginary time correlation function for quantum spins calculated. These corrections qualitatively change the low temperature behaviour for large rho . In particular the corrections to the SA result in the entropy vanishing exponentially as the temperature tends to zero. They compute the finite rho changes in the phase diagram, and discuss the emergence of a new critical point ending the transition line separating the two paramagnetic phases.

Journal of Physics A Mathematical and General•Aug 7, 1990•35 citations
The phase diagram of the ppp-spin-interacting spin glass model in a transverse field is investigated in the limit p→∞p \to \inftyp→∞ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p→∞p \to \inftyp→∞ by using the large-ppp expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.
The phase diagram of the ppp-spin-interacting spin glass model in a transverse field is investigated in the limit p→∞p \to \inftyp→∞ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p→∞p \to \inftyp→∞ by using the large-ppp expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.
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.
The infinite-range Ising spin glass in the presence of a transverse field is considered. Using the generalised Trotter formula and replica methods, the free energy for the system with quenched random bond interactions is evaluated using the static approximation. It is shown that, when the strength of the transverse field equals the largest eigenvalue of the random bond interaction matrix, the spin glass transition is destroyed. The authors also show that a replica-symmetric spin glass phase is stable in a certain region of the temperature-field phase diagram. Finally they present suggestive arguments which indicate that, when the time dependence of the dynamic susceptibility is included, then the stability of the replica-symmetric phase is enhanced.
We analyze the zero-temperature phase diagram of two kinds of one-dimensional quantum-spin models in a transverse magnetic field. The first kind has uniform nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic couplings. A spin-wave analysis indicates the presence of several (possibly an infinite number of) commensurate modulated phases in the phase diagram. The three most prominent phases are paramagnetic, ferromagnetic, and a q=(1/4 phase of period four. The second kind of model is a spin-glass with only nearest-neighbor ferromagnetic interactions whose strengths are random and are characterized by a probability function. A classical large-S analysis shows the existence of a Griffiths phase lying in between a low-magnetic-field ferromagnetic phase and a high-magnetic-field paramagnetic phase. We present two order parameters that can together distinguish between the three phases.
The authors develop systematic 1/ rho expansions for the rho -spin interaction spin-glass model in a transverse field. This model can be solved using the static approximation (SA), which is expected to be valid in the limit rho to infinity . For large, but finite rho , corrections to SA can be obtained, and the non-trivial time dependence of the imaginary time correlation function for quantum spins calculated. These corrections qualitatively change the low temperature behaviour for large rho . In particular the corrections to the SA result in the entropy vanishing exponentially as the temperature tends to zero. They compute the finite rho changes in the phase diagram, and discuss the emergence of a new critical point ending the transition line separating the two paramagnetic phases.