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physica status solidi (b)

Central peak in ising model with transverse field

V. N. Kashcheev

Published Aug 1, 1979• 7 citations
Publisher

Abstract

Abstract The momentum and temperature dependence of the central peak (CP) width is found for the Ising model with a transverse field in the right neighbourhood of the Curie point. The width of CP in the critical and hydrodynamic limits is described by a scaling‐type relation. During deuteration the width of CP diminishes as a squared tunneling frequency.

DOI
10.1002/pssb.2220940246

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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.

physica status solidi (b)•Dec 1, 1977•23 citations
Abstract The momentum and temperature dependence of the central peak (CP) width is found for the Ising model with a transverse field in the right neighbourhood of the Curie point. The width of CP in the critical and hydrodynamic limits is described by a scaling‐type relation. During deuteration the width of CP diminishes as a squared tunneling frequency.
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.
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.