The infinite-range quantum Ising spin-glass model in a transverse field \ensuremath{\Gamma} is studied within the cluster-expansion method formulated originally for spin systems by Morita and Tanaka. With use of the pair approximation, the mean-field equation and condition for critical values of ${\ensuremath{\Gamma}}_{c}$ and ${T}_{c}$ are obtained including the case ${T}_{c}$ \ensuremath{\rightarrow}0.The infinite-range quantum Ising spin-glass model in a transverse field \ensuremath{\Gamma} is studied within the cluster-expansion method formulated originally for spin systems by Morita and Tanaka. With use of the pair approximation, the mean-field equation and condition for critical values of ${\ensuremath{\Gamma}}_{c}$ and ${T}_{c}$ are obtained including the case ${T}_{c}$\ensuremath{\rightarrow}0.

Physical review. B, Condensed matterJul 1, 198826 citations

Instabilities in the quantum Sherrington-Kirkpatrick Ising spin glass in transverse and longitudinal fields

T. K. Kopeć, Klaus D. Usadel, G. Büttner

The infinite-range quantum Ising spin glass in transverse ($\ensuremath{\Gamma}$) and longitudinal ( $h$ ) fields is studied by means of thermo-field-dynamics as a substitute for the $n$ -replica trick. With the use of a one-loop approximation for the dynamic self-interaction the stability of the mean-field-type solution against the action of fluctuations is investigated in the parameter space (${k}_{B}T, \ensuremath{\Gamma}, h$).The infinite-range quantum Ising spin glass in transverse ($\ensuremath{\Gamma}$) and longitudinal ($h$) fields is studied by means of thermo-field-dynamics as a substitute for the $n$-replica trick. With the use of a one-loop approximation for the dynamic self-interaction the stability of the mean-field-type solution against the action of fluctuations is investigated in the parameter space (${k}_{B}T, \ensuremath{\Gamma}, h$).

Physical review. B, Condensed matterJun 1, 198945 citations

Quantum spin glasses in the Ising model with a transverse field

Ya. V. Fedorov, E. F. Shender

ZhETF Pisma RedaktsiiuJun 1, 19862 citations

Quantum Critical Behavior of the Infinite-range Transverse Ising Spin Glass : An Exact Numerical Diagonalization Study

Parongama Sen, Purusattam Ray, Bikas K. Chakrabarti

We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field $Γ$ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of $Γ$ and for system sizes $N \le 16$ . We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of $Γ$ . The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at $Γ_c \simeq 1.5$ . Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get $z=2.1 \pm 0.1$ which is in contradiction with a recent estimate ( $z=4$ ). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for $Γ< Γ_c$ .We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field $Γ$ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of $Γ$ and for system sizes $N \le 16$. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of $Γ$. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at $Γ_c \simeq 1.5$. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get $z=2.1 \pm 0.1$ which is in contradiction with a recent estimate ($z=4$). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for $Γ< Γ_c$.

arXiv:cond-mat/9705297May 29, 19970 citations

{T}_{c}

are obtained including the case

{T}_{c}

\ensuremath{\rightarrow}0.

The infinite-range quantum Ising spin glass in transverse ($\ensuremath{\Gamma}$) and longitudinal (

h

) fields is studied by means of thermo-field-dynamics as a substitute for the

n

-replica trick. With the use of a one-loop approximation for the dynamic self-interaction the stability of the mean-field-type solution against the action of fluctuations is investigated in the parameter space (${k}_{B}T, \ensuremath{\Gamma}, h$).

We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field

Γ

at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of

Γ

and for system sizes

N \le 16

. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of

Γ

. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at

Γ_c \simeq 1.5

. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get

z=2.1 \pm 0.1

which is in contradiction with a recent estimate (

z=4

). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for

Γ< Γ_c