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Annals of Physics

Dynamic behavior of a spin system with small transverse coupling under the influence of an oscillating magnetic field

Paul H. E. Meijer, John C. Edwards

Published Sep 1, 1969• 6 citations
Publisher
DOI
10.1016/0003-4916(69)90152-3

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In this letter, we have studied the influence of the external magnetic fields on tunneling of the spin-1 Bose condensate. We find that the population transfer between spin-0 and spin-±1 exhibits the step structure under the external cosinusoidal magnetic field and a combination of static and cosinusoidal one, respectively. Compared with the longitudinal component of the external magnetic field, the smaller the transverse component of the magnetic field is, the larger the time scale of exhibiting the step structure does. The tunneling current may exhibit periodically oscillation behavior when the ratio of the transverse component of the magnetic field is smaller than that of the longitudinal component, otherwise it exhibits a damply oscillating behavior. This means that the dynamical spin localization can be adjusted by the external magnetic fields.
Applying the master equation to an Ising model, equations of motion are obtained for the average of a single spin and for the average of a pair of spins. These equations relax to equilibrium values that predict a self-consistency relationship among the internal field, temperature, and exchange energy. The critical temperature obtained is that of the Bethe approximation, and is extended to include a static external field in the magnetization direction. With this, the relaxation of an Ising model near the Curie temperature has been investigated in a self-consistent manner. The results are similar to those of Suzuki and Kubo, but in the Bethe approximation instead of the Bragg-Williams approximation, and hence predict the relaxation of the correlation as well. In particular we studied a nearly Ising spin system that is a system with relatively small isotropic transverse coupling. An oscillating, linear, and external magnetic field applied transverse to the strongly coupled direction of the spins leads to lowering of the critical temperature.
The effects of Gaussian disorder on the dynamics of the one-dimensional spin-1/2 random transverse Ising model are studied in the high-temperature limit by the recursion method. Both spin autocorrelation functions and the corresponding spectral densities are calculated for three types of disordered cases. It is found that when the standard deviation ${\ensuremath{\sigma}}_{J}$ of the exchange coupling (or the standard deviation ${\ensuremath{\sigma}}_{B}$ of the random transverse field) is small, the dynamics of the system undergoes two crossovers in sequence as the mean value of the exchange coupling (or the random transverse field) varies: from a central-peak behavior to a collective-mode one, and then to the precession of free spins in an external transverse magnetic field. However, when ${\ensuremath{\sigma}}_{J}$ or ${\ensuremath{\sigma}}_{B}$ are large enough, there is no crossover, i.e., the dynamics of the system shows a central-peak behavior and a disordered behavior, respectively.