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 the Physical Society of Japan

The Ising Model with a Transverse Field

Kazuo Hattori

Published Jul 15, 1977• 13 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.43.77

Related papers

The Ising model with a transverse field. I. High temperature expansion

Roger James Elliott, C Wood

The Ising model (exchange constant J) with a transverse field Gamma can be regarded as a simple model of hydrogen bonded ferroelectrics and of certain magnetic systems. The transition temperature T C decreases as Gamma increases and falls to zero at a critical field Gamma C . This transition is studied in the quadratic and simple cubic lattices with nearest neighbour interactions by a power series expansion of the susceptibility at high T up to fifth order in (J/kT) to all orders in ( Gamma /kT). The coefficients are calculated by diagram counting and time ordering perturbation methods. The critical Gamma against T curve is derived and the critical exponent gamma of the susceptibility. This appears to vary smoothly with Gamma but it is argued that this is an artifact due to the use of a short series and that the critical exponents are probably independent of Gamma as long as T C remains finite but change discontinuity at T C =0.

Journal of Physics C Solid State Physics•Oct 28, 1971•121 citations

Static Properties of the Transverse Ising Model with Substitutional Disorder

Kazushige Mori

On the basis of the effective Hamiltonian method the static properties of the transverse Ising model with substitutional disorder have been investigated. By a perturbation expansion of the density matrix the self-consistent equation for the effective field is obtained in an analytical form. The transition temperature and the susceptibility etc. are derived from the partition function and numerically calculated. It is shown that for the diluted systems this approximation gives much lower transition temperatures and higher critical concentrations than the simple ones previously derived. In the two-component system with a strong transverse field a finite critical concentration is predicted in contrast to the previous studies. The application of this approximation to the “pseudo” one-dimensional systems having weak interchain correlations is also discussed.

Journal of the Physical Society of Japan•Nov 1, 1981•2 citations

The transverse Ising model in the paid approximation

Terufumi Yokota

The transverse Ising model is investigated in the pair approximation. Critical lines for an arbitrary number of nearest-neighbour spins can be obtained. Using the approximation, Suzuki's coherent anomaly method is applied to the model and critical exponents of the susceptibility are estimated and compared with the real values. The agreement is not excellent for the small size of the cluster used and the author concludes that larger clusters are necessary for a reliable estimate for the critical exponents by this method.

Journal of Physics C Solid State Physics•Dec 20, 1988•19 citations

The diluted transverse Ising model

T. Kaneyoshi

Two effective-field treatments are presented for the diluted transverse Ising model. The methods include the effects of correlation. The critical temperature, the longitudinal and transverse magnetisations, the initial transverse susceptibility and the two-site spin correlation function are calculated for a square lattice. It was found that, in particular, the transverse magnetisation and the initial transverse susceptibility exhibit behaviour which is interesting in the diluted case.

Journal of Physics C Solid State Physics•Jun 10, 1986•25 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

Phase Diagrams of the Transverse Ising Model with Anisotropic Crystal-Field

Wei Hua Guo

The spin 3/2 transverse Ising model with anisotropic crystal field on honeycomb lattice (z=3) has been studied by using the effective field theory with correlations. The general expressions for evaluating the second order phase transition temperatures are obtained. The results show that both the transverse field and crystal field have important effects on the phase diagram of the Ising system. The transition temperatures do not always fall to zero when Ω/|J|0 457. They approach a constant value 0 525 for large negative D(D→-∞) without transverse field (Ω=0). On the other hand, it is shown that all phase transformations are second order.

Journal of Northeastern University•Jan 1, 2000•0 citations
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.
The Ising model (exchange constant J) with a transverse field Gamma can be regarded as a simple model of hydrogen bonded ferroelectrics and of certain magnetic systems. The transition temperature T C decreases as Gamma increases and falls to zero at a critical field Gamma C . This transition is studied in the quadratic and simple cubic lattices with nearest neighbour interactions by a power series expansion of the susceptibility at high T up to fifth order in (J/kT) to all orders in ( Gamma /kT). The coefficients are calculated by diagram counting and time ordering perturbation methods. The critical Gamma against T curve is derived and the critical exponent gamma of the susceptibility. This appears to vary smoothly with Gamma but it is argued that this is an artifact due to the use of a short series and that the critical exponents are probably independent of Gamma as long as T C remains finite but change discontinuity at T C =0.
On the basis of the effective Hamiltonian method the static properties of the transverse Ising model with substitutional disorder have been investigated. By a perturbation expansion of the density matrix the self-consistent equation for the effective field is obtained in an analytical form. The transition temperature and the susceptibility etc. are derived from the partition function and numerically calculated. It is shown that for the diluted systems this approximation gives much lower transition temperatures and higher critical concentrations than the simple ones previously derived. In the two-component system with a strong transverse field a finite critical concentration is predicted in contrast to the previous studies. The application of this approximation to the “pseudo” one-dimensional systems having weak interchain correlations is also discussed.
The transverse Ising model is investigated in the pair approximation. Critical lines for an arbitrary number of nearest-neighbour spins can be obtained. Using the approximation, Suzuki's coherent anomaly method is applied to the model and critical exponents of the susceptibility are estimated and compared with the real values. The agreement is not excellent for the small size of the cluster used and the author concludes that larger clusters are necessary for a reliable estimate for the critical exponents by this method.
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 spin 3/2 transverse Ising model with anisotropic crystal field on honeycomb lattice (z=3) has been studied by using the effective field theory with correlations. The general expressions for evaluating the second order phase transition temperatures are obtained. The results show that both the transverse field and crystal field have important effects on the phase diagram of the Ising system. The transition temperatures do not always fall to zero when Ω/|J|0 457. They approach a constant value 0 525 for large negative D(D→-∞) without transverse field (Ω=0). On the other hand, it is shown that all phase transformations are second order.