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Journal of Physics Condensed Matter

Dynamic structure factor of the transverse Ising model

J. Florencio, Surajit Sen, Zhi-Xiong Cai

Published Feb 13, 1995• 9 citations
Publisher

Abstract

We report the first analytic study of real time and frequency dependent behaviour at T= infinity of the 2D square lattice transverse Ising model. Our study, along with known results in the 1D case, in the mean field or infinity D case and in other studies, helps understand the experimentally obtained longitudinal dynamic structure factor of the induced moment ferromagnet LiTbF 4 studied by Youngblood et al., and is consistent with the studies of Kotzler et al.

DOI
10.1088/0953-8984/7/7/017

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We report the first analytic study of real time and frequency dependent behaviour at T= infinity of the 2D square lattice transverse Ising model. Our study, along with known results in the 1D case, in the mean field or infinity D case and in other studies, helps understand the experimentally obtained longitudinal dynamic structure factor of the induced moment ferromagnet LiTbF 4 studied by Youngblood et al., and is consistent with the studies of Kotzler et al.
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.
We have considered a numerical scheme for the calculation of the equilibrium properties of spin-1/2 XY chains. Within its frames it is necessary to solve in the last resort only the 2N\times 2N eigenvalue and eigenvector problem but not the 2^N\times 2^N one as for an arbitrary system consisting of N spins 1/2. To illustrate the approach we have presented some new results. Namely, the xx dynamic structure factor for the Ising model in transverse field, the density of states for the isotropic chain with random intersite couplings and transverse fields that linearly depend on the surrounding couplings, and the zz dynamic structure factor for the Ising model in random transverse field. The results obtained are hopped to be useful for an interpretation of observable data for one-dimensional spin-1/2 XY substances.
The critical behaviour of the spin- Ising model with a transverse field at zero temperature in triangular and square lattices is investigated through a finite-size rescaling transformation. This technique enables the critical properties of infinite systems to be calculated from the scaling properties of systems of finite size, in a generalisation of the so-called phenomenological renormalisation group. The critical field and correlation length exponent calculated using systems of fairly small sizes have reasonable accuracy, but calculations on larger clusters are limited by computer time and storage.
The dynamic structure factor of the spin-12\frac{1}{2}21​ transverse Ising chain is obtained by means of a numerical approach suggested earlier [O. Derzhko and T. Krokhmalskii, Ferroelectrics 192, 21 (1997)]. Frequency shapes of the dynamic structure factor at various values of the wave vector, transverse field, and temperature are displayed and discussed.