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

Dynamics of the two-sublattice Ising model in a transverse field studied using a coupled-operators continued-fraction expansion

C E SaMotta, Antonio S. T. Pires

Published Nov 20, 1984• 1 citation
Publisher

Abstract

The dynamics of the longitudinal spin fluctuations of the two-sublattice three-dimensional Ising model in a transverse field is studied using a continued-fraction expansion for coupled operators.
DOI
10.1088/0022-3719/17/32/010

Related papers

A continued-fraction representation for the one-dimensional transverse Ising model

J. A. Plascak, F. C. Sá Barreto, Antonio S. T. Pires +1 more

The dynamics of the one-dimensional transverse Ising mode is studied by means of Mori's continued-fraction representation in the three- and four-pole approximations. The required moments are obtained using the longitudinal time-dependent correlation function calculated in the c-cyclic approximation and various cut-offs of the continued-fraction representation are analysed.

Journal of Physics C Solid State Physics•Jan 10, 1983•15 citations

Dynamics of the strong anisotropic three-dimensional Ising model in a transverse field

J. A. Plascak, F. C. Sá Barreto, Antonio S. T. Pires

The dynamics of the three-dimensional anisotropic spin-\textonehalf{} Ising model in a transverse field is studied above ${T}_{c}$ by a method in which the coupled-chain problem is reduced to that of a single chain in an effective field. The problem of a single chain is studied by means of Mori's continued-fraction expansion in a four-pole approximation. The moments are obtained by using the time-dependent correlation function calculated in the $c$-cyclic and in the improved $c$-cyclic approximations [J. Phys. A 13, 223 (1980)]. A comparison between these two approximations is done by calculating the critical temperature as function of the tunneling field. The one-dimensional correlation length is obtained, and it agrees well with the experimental results for the quasi-one-dimensional ferroelectric Cs${\mathrm{D}}_{2}$P${\mathrm{O}}_{4}$.

Physical review. B, Condensed matter•Jan 1, 1983•16 citations

Dynamics of the random one-dimensional transverse Ising model

J. Florencio, F. C. Sá Barreto

We study the dynamics of the spin-1/2 random transverse Ising model in the high-temperature limit by means of the method of recurrence relations. We analyze two types of disorder: a disorder on the transverse field, and a disorder on the exchange coupling. We find that the dynamics undergoes a crossover from a central peak behavior onto a collective mode behavior as a function of the disorder.

Physical review. B, Condensed matter•Oct 1, 1999•34 citations

Dynamics of the Iongitudinal spin for the three-dimensional, spin-½ Ising model in a transverse field

T. N. Tommet, David L. Huber

The dynamics of the Iongitudinal (i.e., parrallel to the $z$ axis) spin fluctuations of the three-dimensional Ising model in a transverse field, $H=\ensuremath{-}\ensuremath{\Gamma}\ensuremath{\Sigma}{i}^{}{S}_{i}^{x}\ensuremath{-}(\frac{1}{2})\ensuremath{\Sigma}{\mathrm{ij}}^{}{J}_{\mathrm{ij}}{S}_{i}^{z}{S}_{j}^{z}$, is studied. An approximate expression for the relaxation shape function is given which gives a simple but realistic view of the dynamics for the entire temperature range ${T}_{c}<T<\ensuremath{\infty}$. Plots of the shape function are obtained and analyzed.

Physical review. B, Solid state•Mar 1, 1975•46 citations

Dynamics and Statistical Mechanics of the Classical Ising Model in a Transverse Field

Shigeo Homma, Shôzô Takeno

Dynamics and the approximate thermodynamical properties of the classical Ising model in a transverse field (CIMTF) are studied. This is done by elucidating a close correspondence of the CIMTF to a nonlinear lattice field in which each atom, while coupled harmonically with its neighbours, sits on on-site anharmonic potential. It is shown that when the ratio of the Ising interaction to a transverse field-strength exceeds a certain critical value, the on-site potential is of double-well type with saturable nonlinearity. Domain wall modes and magnon modes in continuous one-dimensional CIMTF are studied for both systems to substantiate the correspondence. By exploiting this, a brief study is made on the approximate properties of the free energy and of the dynamical structure factor S ( k ,ω) of longitudinal spin fluctuations of the CIMTF. These quantities are shown to be composed of two contributions, one from domain-wall modes and the other from magnon modes, which manifest themselves as a central peak and side peaks in S ( k ,ω), respectively.

Journal of the Physical Society of Japan•Nov 15, 1980•5 citations

Mode-coupling theory for the central peak in the ising model in a transverse field

Peter Prelovšek, Igor Sega

The dynamics of longitudinal spin fluctuations in the S = 1/2 Ising model in a transverse field is studied. Exploiting the mode-coupling approximation for the relaxation function we show that the width of the central peak which appears just above Tc is determined by the nonlinear coupling of fluctuations to the hydrodynamic energy-density mode. The results for the central peak are compared to those obtained within the usual three-pole approximation.

Ferroelectrics•Jan 1, 1980•3 citations
The dynamics of the three-dimensional anisotropic spin-\textonehalf{} Ising model in a transverse field is studied above Tc{T}_{c}Tc​ by a method in which the coupled-chain problem is reduced to that of a single chain in an effective field. The problem of a single chain is studied by means of Mori's continued-fraction expansion in a four-pole approximation. The moments are obtained by using the time-dependent correlation function calculated in the ccc-cyclic and in the improved ccc-cyclic approximations [J. Phys. A 13, 223 (1980)]. A comparison between these two approximations is done by calculating the critical temperature as function of the tunneling field. The one-dimensional correlation length is obtained, and it agrees well with the experimental results for the quasi-one-dimensional ferroelectric CsD2{\mathrm{D}}_{2}D2​PO4{\mathrm{O}}_{4}O4​.
The dynamics of the Iongitudinal (i.e., parrallel to the zzz axis) spin fluctuations of the three-dimensional Ising model in a transverse field, $H=\ensuremath{-}\ensuremath{\Gamma}\ensuremath{\Sigma}{i}^{}{S}_{i}^{x}\ensuremath{-}(\frac{1}{2})\ensuremath{\Sigma}{\mathrm{ij}}^{}{J}_{\mathrm{ij}}{S}_{i}^{z}{S}_{j}^{z}$, is studied. An approximate expression for the relaxation shape function is given which gives a simple but realistic view of the dynamics for the entire temperature range ${T}_{c}<T<\ensuremath{\infty}$. Plots of the shape function are obtained and analyzed.
Dynamics and the approximate thermodynamical properties of the classical Ising model in a transverse field (CIMTF) are studied. This is done by elucidating a close correspondence of the CIMTF to a nonlinear lattice field in which each atom, while coupled harmonically with its neighbours, sits on on-site anharmonic potential. It is shown that when the ratio of the Ising interaction to a transverse field-strength exceeds a certain critical value, the on-site potential is of double-well type with saturable nonlinearity. Domain wall modes and magnon modes in continuous one-dimensional CIMTF are studied for both systems to substantiate the correspondence. By exploiting this, a brief study is made on the approximate properties of the free energy and of the dynamical structure factor S ( k ,ω) of longitudinal spin fluctuations of the CIMTF. These quantities are shown to be composed of two contributions, one from domain-wall modes and the other from magnon modes, which manifest themselves as a central peak and side peaks in S ( k ,ω), respectively.