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

The spin S Ising model with a transverse field

J. Oitmaa, G J Coombs

Published Jan 20, 1981• 25 citations
Publisher

Abstract

The authors have investigated the properties of the Ising model in a transverse field for general spin S by the method of high-temperature series. Analysis of the series yields the form of the phase diagram in the temperature field plane. The authors also investigate the variation of critical field with spin, and present evidence for classical-quantum crossover at T=0 for all spin values.

DOI
10.1088/0022-3719/14/2/011

Related papers

Ising model with a transverse field in two dimensions: Phase diagram and critical properties from a real-space renormalization group

Zvi Friedman

Critical indices, the critical line, and the crossover scaling function for the free energy are calculated for the two-dimensional Ising model with a transverse field using a quantum-mechanical version of the real-space renormalization group. The critical behavior as function of the transverse field at a small finite temperature changes from that of a three-dimensional to that of a two-dimensional Ising behavior, as the critical line is approached.

Physical review. B, Condensed matter•Feb 1, 1978•24 citations

Critical behaviour of the Ising model with a transverse field

J. Oitmaa, Michael Plischke

Ten terms have been obtained in the high-temperature series for the fluctuation in long-range order of the Ising model in a transverse magnetic field on the three cubic lattices. This model is relevant to real materials such as singlet-singlet magnetic systems, hydrogen-bonded ferroelectrics and cooperative Jahn-Teller systems. The critical temperature of the system was obtained over essentially the entire range of the transverse field for which a phase transition exists. No crossover to the expected d=4 critical behaviour was observed at T=0.

Journal of Physics C Solid State Physics•Jun 14, 1976•19 citations

The spin-S quantum Ising model at T=O

G. Kamieniarz, Leon Kowalewski, Włodzimierz Piechocki

The Ising model with a transverse field for a general spin S is investigated within the framework of the Green function method in the paramagnetic region at T=O. The analysis of self-consistent equations gives a description of soft-mode phase transitions as well as extrapolated values of the critical fields and critical energy gap exponents.

Journal of Physics C Solid State Physics•Jul 10, 1983•5 citations

Equation of state and quantum crossover in the transverse Ising model

K. Lukierska‐Walasek

The equation of state of the transverse Ising model in a longitudinal field B is investigated in the vicinity of the zero-temperature multicritical point by using the renormalisation group method recently proposed by the author and K. Walasek (1983). For the critical value of transverse field the scaling crossover form of the relation between the longitudinal magnetic field and magnetisation M is obtained as B approximately M delta q Psi (z) with z approximately TM - phi beta q/, where phi , delta q and beta q denote the crossover and multicritical exponents. The crossover scaling function Psi (z) is calculated for the spatial dimensions d<or=3 and 3<d<4 to the first order in epsilon '=3-d and epsilon =4-d, respectively.

Journal of Physics C Solid State Physics•Oct 30, 1984•2 citations

Properties of the phase transition in the transverse Ising model

L. De Cesare, Ileana Rabuffo, Dimo I. Uzunov

The phase transition properties of the quantum spin{1/2 Ising model in a transverse magnetic eld are reconsidered with the help of the mean eld approximation, the Ginzburg criterion, and the renormalization group theory.A special attention is paid to the phase transitions whose properties are determined by variations of the external transverse eld and to the low{temperature phase transitions due to temperature variations.The classical{to{quantum crossover is investigated in details.A new crossover eect is established and discussed.

Journal of Physical Studies•Jan 1, 1998•1 citation

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
The authors have investigated the properties of the Ising model in a transverse field for general spin S by the method of high-temperature series. Analysis of the series yields the form of the phase diagram in the temperature field plane. The authors also investigate the variation of critical field with spin, and present evidence for classical-quantum crossover at T=0 for all spin values.
Ten terms have been obtained in the high-temperature series for the fluctuation in long-range order of the Ising model in a transverse magnetic field on the three cubic lattices. This model is relevant to real materials such as singlet-singlet magnetic systems, hydrogen-bonded ferroelectrics and cooperative Jahn-Teller systems. The critical temperature of the system was obtained over essentially the entire range of the transverse field for which a phase transition exists. No crossover to the expected d=4 critical behaviour was observed at T=0.
The equation of state of the transverse Ising model in a longitudinal field B is investigated in the vicinity of the zero-temperature multicritical point by using the renormalisation group method recently proposed by the author and K. Walasek (1983). For the critical value of transverse field the scaling crossover form of the relation between the longitudinal magnetic field and magnetisation M is obtained as B approximately M delta q Psi (z) with z approximately TM - phi beta q/, where phi , delta q and beta q denote the crossover and multicritical exponents. The crossover scaling function Psi (z) is calculated for the spatial dimensions d<or=3 and 3<d<4 to the first order in epsilon '=3-d and epsilon =4-d, respectively.
The phase transition properties of the quantum spin{1/2 Ising model in a transverse magnetic eld are reconsidered with the help of the mean eld approximation, the Ginzburg criterion, and the renormalization group theory.A special attention is paid to the phase transitions whose properties are determined by variations of the external transverse eld and to the low{temperature phase transitions due to temperature variations.The classical{to{quantum crossover is investigated in details.A new crossover eect is established and discussed.
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.