Physical review. B, Condensed matter

Cluster-expansion method for the infinite-range quantum transverse Ising spin-glass model

Katarzyna Walasek, K. Lukierska‐Walasek

Published Jul 1, 1988• 26 citations

Abstract

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.

DOI: 10.1103/physrevb.38.725

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Physical review. B, Condensed matter

Cluster-expansion method for the infinite-range quantum transverse Ising spin-glass model

Katarzyna Walasek, K. Lukierska‐Walasek

Published Jul 1, 1988• 26 citations

Publisher

Abstract

{\ensuremath{\Gamma}}_{c}

and

{T}_{c}

are obtained including the case

{T}_{c}

\ensuremath{\rightarrow}0.

DOI: 10.1103/physrevb.38.725

Related papers

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

Terufumi Yokota

Physical review. B, Condensed matterNov 1, 198916 citations

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Katarzyna Walasek, K. Lukierska‐Walasek, L. De Cesare +1 more

The classical transverse field Ising spin-glass model with short-range interactions is investigated beyond the mean-field approximation for a real d -dimensional lattice. We use an appropriate non-trivial modification of the Bethe-Peierls method recently formulated for the Ising spin-glass. The zero-temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d . The phase diagram is also calculated numerically for different values of d . In the limit , known mean-field results are consistently reproduced.The classical transverse field Ising spin-glass model with short-range interactions is investigated beyond the mean-field approximation for a real d -dimensional lattice. We use an appropriate non-trivial modification of the Bethe-Peierls method recently formulated for the Ising spin-glass. The zero-temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d . The phase diagram is also calculated numerically for different values of d . In the limit , known mean-field results are consistently reproduced.

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Jonathan Miller, David A. Huse

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Physical Review LettersMay 17, 1993136 citations

{\ensuremath{\Gamma}}_{c}

and

{T}_{c}

are obtained including the case

{T}_{c}

\ensuremath{\rightarrow}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.

An infinite-range transverse-field Ising spin glass is studied in the classical limit. At the

T=0

phase transition the nonlinear susceptibility diverges as a function of the field with an exponent of

1/2

which is equal to the quantum estimates but without a multiplicative logarithmic correction. The replica-symmetric solution fails at

T=0

below the critical value of the transverse field. Equations that break the replica symmetry are constructed and are shown to be harder to solve than in the absence of the transverse field. In the absence of the transverse field their solution agrees with that of Sommers and Dupont [J. Phys. C 17, 5785 (1984)].