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

Journal of Physics C Solid State Physics

Temperature dependence of the transverse spin in the transverse Ising model

Lui Lam, Armin Bunde A

Published Mar 14, 1977• 6 citations
Publisher

Abstract

Rigorous upper and lower bounds on the temperature dependence of the transverse spin in the transverse Ising model are calculated. The mean field approximation is shown to be identical to the lower bound in the limit of strong transverse field. Other approximate and sometimes conflicting calculations in the literature as well as experimental results are discussed and compared with the authors' exact bounds.

DOI
10.1088/0022-3719/10/5/013

Related papers

Correlation equalities and upper bounds for the transverse Ising model

F C Sá Barreto, A L Mota

Starting from an exact formal identity for the two-state transverse Ising model and using correlation inequalities, approximate upper bounds for the critical temperature and the critical transverse field are obtained, which improve the effective results.

arXiv:1202.2237•Journal of Statistical Mechanics Theory and Experiment•May 11, 2012•8 citations

A Study of the Transverse Ising Model

Jialin Zhong, Chuan‐Zhang Yang, Xuefan Jiang

Abstract A new method which combines the discretized path‐integral with variational approximation is proposed and used to derive the free energy of the transverse Ising model in a quantum spin system. The transition temperature dependence of both, the transverse field and the coordination number is obtained analytically. The numerical results are compared with those of other methods.

physica status solidi (b)•Oct 1, 1991•1 citation

The Ising Model with a Transverse Field

Kazuo Hattori

The Ising model with a transverse field has been investigated for both positive and negative exchange interactions. Effective Hamiltonians are used for a pair of nearest-neighbour spins. The transition temperature and susceptibility above the transition temperature are calculated. The critical magnitude of the transverse field for which the transition temperature becomes 0 K is also evaluated. When the transverse field is absent, the result of the present method is reduced to that of the Bethe approximation.

Journal of the Physical Society of Japan•Jul 15, 1977•13 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

Classical transverse Ising spin glass with short-range interactions beyond the mean-field approximation

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.

arXiv:cond-mat/9804033•Journal of Physics A Mathematical and General•Jul 10, 1998•3 citations

Dynamics of the one-dimensional transverse Ising model

L.L. Gonçalves

An approximate expression for the time-dependent longitudinal correlation function is given. It gives exact results in the limiting cases where the transverse field, or the exchange interaction, is zero. It is also shown that for arbitrary values of these parameters the approximation is only valid in the high-temperature limit. Some results are presented for the time-dependent and frequency transform of the spatial Fourier transform.

Journal of Physics A Mathematical and General•Jan 1, 1980•5 citations
Rigorous upper and lower bounds on the temperature dependence of the transverse spin in the transverse Ising model are calculated. The mean field approximation is shown to be identical to the lower bound in the limit of strong transverse field. Other approximate and sometimes conflicting calculations in the literature as well as experimental results are discussed and compared with the authors' exact bounds.
The Ising model with a transverse field has been investigated for both positive and negative exchange interactions. Effective Hamiltonians are used for a pair of nearest-neighbour spins. The transition temperature and susceptibility above the transition temperature are calculated. The critical magnitude of the transverse field for which the transition temperature becomes 0 K is also evaluated. When the transverse field is absent, the result of the present method is reduced to that of the Bethe approximation.
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 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.