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physica status solidi (b)

Effects of the BijSxiSxj Interaction on the IMTF's Dynamics

Antônio Tarciso Borges, L. A. Amarante Ribeiro

Published Aug 1, 1984• 0 citations
Publisher

Abstract

Abstract Additively to the Ising model in a transverse field (IMTF) an interaction BijS S is considered. For a S = 1/2 three‐dimensional cubic latticethe longitudinal relaxation shape function is calculated by means of Mori's continued‐fraction representation in a three‐pole approximation. The effects of this new term on the fluctuation spectra are studied for T > Tc and the results compared with those obtained for the pure IMTF.

DOI
10.1002/pssb.2221240238

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physica status solidi (b)•Dec 1, 1977•23 citations
Abstract Additively to the Ising model in a transverse field (IMTF) an interaction BijS S is considered. For a S = 1/2 three‐dimensional cubic latticethe longitudinal relaxation shape function is calculated by means of Mori's continued‐fraction representation in a three‐pole approximation. The effects of this new term on the fluctuation spectra are studied for T > Tc and the results compared with those obtained for the pure IMTF.
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.
We derive the moments, at $T=\ensuremath{\infty}$, of the longitudinal spin-spin correlation function of the Ising model in a transverse field. The first 20 moments are obtained for the linear chain, the first 12 moments for the fcc lattice. We use a method of Nickel [J. Phys. C 7, 1719 (1914)] to construct the relaxation function and find excellent agreement with the exact results of Capel and Perk [Physica (Utrecht) 87A, 211 (1977)] in one dimension and extremely good convergence in three dimensions. Our method of analysis provides much better convergence than methods based on truncation of the continued-fraction representation.
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.