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physica status solidi (b)

Damping of the Transverse and Longitudinal Excitations of the Ising Model in a Transverse Field

Julia Mihailowa Wesselinowa

Published Jan 1, 1984• 8 citations
Publisher

Abstract

Abstract The Ising model in a transverse field is treated by means of the Green function technique to calculate the excitation spectrum and the damping of these excitations above and below Tc. The soft mode is overdamped in the disordered phase and near Tc, while it is nearly undamped at low temperatures. The temperature dependence of the transverse and longitudinal damping for zero wave vector is calculated numerically for different values of the transverse field.

DOI
10.1002/pssb.2221210134

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Progress of Theoretical Physics•Nov 1, 1978•5 citations
Abstract The Ising model in a transverse field is treated by means of the Green function technique to calculate the excitation spectrum and the damping of these excitations above and below Tc. The soft mode is overdamped in the disordered phase and near Tc, while it is nearly undamped at low temperatures. The temperature dependence of the transverse and longitudinal damping for zero wave vector is calculated numerically for different values of the transverse field.
Abstract The Ising model in a transverse field is treated by means of Green function technique to calculate the dynamic structure factor above and below Tc. The soft mode is overdamped in the disordered phase and near Tc, while it is nearly undamped at low temperatures. The coupling between the transverse soft mode and the relaxing longitudinal mode produces a central mode in the dynamic structure factor. The temperature dependence of the dynamic structure factor for zero wave vector is calculated numerically.
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 Ising Model in a transverse field is investigated employing a field theoretical diagrammatic technique. The diagrams are classified with respect to a high density parameter 1/z, where z is the number of spins interacting with a given spin. The energy spectrum of collective excitations has been obtained both in the disordered phase and in the ordered phase. Summation of the chain diagrams (of order 1) reproduces the previous results. We have calculated the contributions of all diagrams of order 1/z and showed that the RPA commonly used has failed to include consistently a class of diagrams which reflect the kinematics of spin operators. The damping of the excitation waves is also obtained.