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Physical Review B

Crossover of the dynamical behavior in two-dimensional random transverse Ising model

Shu-Xia Chen, Yin-Yang Shen, Xiang-Mu Kong

Published Nov 3, 2010• 25 citations
Publisher

Abstract

The dynamics of the two-dimensional spin-$\frac{1}{2}$ random transverse Ising model is studied by means of the recurrence relations method. Both the autocorrelation functions and the corresponding spectral densities are calculated in the cases that the exchange couplings or fields satisfy three typical distributions, respectively. For the cases of Gaussian and double-Gaussian distribution, when the standard deviation of the random variable is small, the dynamics of the system undergoes a crossover from a central-peak behavior to a collective-mode one, the result is similar to that of the bimodal distribution. While the standard deviation is large enough, the crossover disappears and the dynamics of the system shows a central-peak behavior or a disordered behavior.

DOI
10.1103/physrevb.82.174404

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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.
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In this paper, the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied. By means of the recurrence relation method in the high-temperature limit, we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution. It is found that when the standard deviation of random exchange coupling δ J (or the standard deviation of random external field δ B ) is small, the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. However, when δ J (or δ B ) is large, the crossover vanishes, and the system shows a central-peak behavior or the most disordered one. We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions. Our results show that for all the cases considered, the dynamics of the above system is similar to that of the one-dimensional random XY model.