Physical Review B

First-order quantum phase transition in an anisotropic Ising model with infinite-range random interaction

J. Roberto Viana, Angsula Ghosh, J. Ricardo de Sousa

Published Jan 23, 2008• 2 citations

Abstract

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 (${D}_{x}$ and ${D}_{y}$) and transverse field $(\ensuremath{\Omega})$ on the phase diagrams in the $T\ensuremath{-}{D}_{x}$ plane for various values of ${D}_{y}$ and $\ensuremath{\Omega}$. Tricritical and reentrant behavior can be seen for appropriate ranges of these parameters.

DOI: 10.1103/physrevb.77.024424

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Physical Review B

First-order quantum phase transition in an anisotropic Ising model with infinite-range random interaction

J. Roberto Viana, Angsula Ghosh, J. Ricardo de Sousa

Published Jan 23, 2008• 2 citations

Publisher

Abstract

{D}_{x}

and

{D}_{y}

) and transverse field

(\ensuremath{\Omega})

on the phase diagrams in the

T\ensuremath{-}{D}_{x}

plane for various values of

{D}_{y}

and

\ensuremath{\Omega}

. Tricritical and reentrant behavior can be seen for appropriate ranges of these parameters.

DOI: 10.1103/physrevb.77.024424

Related papers

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.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.

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{D}_{x}

and

{D}_{y}

) and transverse field

(\ensuremath{\Omega})

on the phase diagrams in the

T\ensuremath{-}{D}_{x}

plane for various values of

{D}_{y}

and

\ensuremath{\Omega}

. Tricritical and reentrant behavior can be seen for appropriate ranges of these parameters.

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.

{h}_{0}

{\mathit{T}}_{\mathit{c}}

vs transverse field \ensuremath{\Gamma}) we obtain shows a finite slope near T=0, in contrast with the infinite slope for the pure case. Our results compare very well with the experimental data recently obtained for the dipolar Ising spin glass

{\mathrm{LiHo}}_{0.167}

{\mathrm{Y}}_{0.833}

{\mathrm{F}}_{4}

, in a transverse field. This indicates that this system is more appropriately described by a model with short-range interactions than by an equivalent Sherrington-Kirkpatrick model in a transverse field.