Journal of Physics C Solid State Physics

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

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

Published Jan 10, 1983• 15 citations

Abstract

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.

DOI: 10.1088/0022-3719/16/1/009

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Journal of Physics C Solid State PhysicsNov 20, 19841 citation

Journal of Physics C Solid State Physics

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

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

Published Jan 10, 1983• 15 citations

Publisher

Abstract

DOI: 10.1088/0022-3719/16/1/009

Related papers

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 ${\mathrm{O}}_{4}$ .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${\mathrm{O}}_{4}$.

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Peter Prelovšek, Igor Sega

The molecular-dynamics technique is applied to the study of the classical ($S=\ensuremath{\infty}$) Ising model in a transverse field on a simple-cubic lattice. The results for the longitudinal- and transverse-relaxation shape function are presented for a set of temperatures in the disordered phase at one value of the transverse field. The longitudinal spectra at $T=\ensuremath{\infty}$ and in the critical regime are analyzed via the Mori's continued-fraction expansion and compared with various approximate results within this approach. The relation of the observed central mode to a domain-wall motion is also discussed. However, due to heavy-damping phenomena no well-defined propagating modes are observed in the critical region. Finally, transverse correlation functions are tested against their diffusive character.The molecular-dynamics technique is applied to the study of the classical ($S=\ensuremath{\infty}$) Ising model in a transverse field on a simple-cubic lattice. The results for the longitudinal- and transverse-relaxation shape function are presented for a set of temperatures in the disordered phase at one value of the transverse field. The longitudinal spectra at $T=\ensuremath{\infty}$ and in the critical regime are analyzed via the Mori's continued-fraction expansion and compared with various approximate results within this approach. The relation of the observed central mode to a domain-wall motion is also discussed. However, due to heavy-damping phenomena no well-defined propagating modes are observed in the critical region. Finally, transverse correlation functions are tested against their diffusive character.

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Memory functions for the one-dimensional Ising model in a transverse field

J. Oitmaa, I. Liubarsky, M. Aydin

We have computed the sequence of memory functions ${K}_{n}$ (t) and their Laplace transforms, for the one-dimensional Ising model in a transverse field at T=\ensuremath{\infty}. The form of these functions shows explicitly why the Mori continued-fraction approach, with traditional truncation schemes, fails for this model.We have computed the sequence of memory functions ${K}_{n}$(t) and their Laplace transforms, for the one-dimensional Ising model in a transverse field at T=\ensuremath{\infty}. The form of these functions shows explicitly why the Mori continued-fraction approach, with traditional truncation schemes, fails for this model.

Physical review. B, Condensed matterSep 1, 19895 citations

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

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.

Journal of Physics C Solid State PhysicsNov 20, 19841 citation

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}

{\mathrm{O}}_{4}

We have computed the sequence of memory functions

{K}_{n}

(t) and their Laplace transforms, for the one-dimensional Ising model in a transverse field at T=\ensuremath{\infty}. The form of these functions shows explicitly why the Mori continued-fraction approach, with traditional truncation schemes, fails for this model.