The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder

doi:10.1088/1674-1056/23/8/087505

中国物理B ›› 2014, Vol. 23 ›› Issue (8): 87505-087505.doi: 10.1088/1674-1056/23/8/087505

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇下一篇

The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder

刘中强, 姜素蓉, 孔祥木

College of Physics and Engineering, Qufu Normal University, Qufu 273165, China

收稿日期:2014-01-03 修回日期:2014-03-26 出版日期:2014-08-15 发布日期:2014-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11302118 and 11275112), the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2013AQ015 and ZR2011AM018), and the Postdoctoral Science Foundation of Qufu Normal University (Grant No. BSQD2012053).

The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder

Liu Zhong-Qiang (刘中强), Jiang Su-Rong (姜素蓉), Kong Xiang-Mu (孔祥木)

College of Physics and Engineering, Qufu Normal University, Qufu 273165, China

Received:2014-01-03 Revised:2014-03-26 Online:2014-08-15 Published:2014-08-15
Contact: Liu Zhong-Qiang E-mail:phyzhqliu@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11302118 and 11275112), the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2013AQ015 and ZR2011AM018), and the Postdoctoral Science Foundation of Qufu Normal University (Grant No. BSQD2012053).

摘要/Abstract

摘要： The dynamical properties of one-dimensional random transverse Ising model (RTIM) with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function (SAF) and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σ_J (or σ_B) of the exchange couplings J_i (or the random transverse fields B_i) is small, no long-time tail appears in the SAF. The spin system undergoes a crossover from a central-peak behavior to a collective-mode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σ_J (or σ_B) is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σ_J or a disordered behavior for large σ_B. In this instance, SAFs exhibit a similar long-time tail, i.e., C(t)～ t^-2 for large t. Similar properties are obtained when J_i (or B_i) satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state.

关键词: random transverse Ising model, spin autocorrelation function, spectral density, long-time tail

Abstract: The dynamical properties of one-dimensional random transverse Ising model (RTIM) with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function (SAF) and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σ_J (or σ_B) of the exchange couplings J_i (or the random transverse fields B_i) is small, no long-time tail appears in the SAF. The spin system undergoes a crossover from a central-peak behavior to a collective-mode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σ_J (or σ_B) is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σ_J or a disordered behavior for large σ_B. In this instance, SAFs exhibit a similar long-time tail, i.e., C(t)～ t^-2 for large t. Similar properties are obtained when J_i (or B_i) satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state.

Key words: random transverse Ising model, spin autocorrelation function, spectral density, long-time tail

中图分类号: (Spin chain models)

75.10.Pq

75.40.Gb (Dynamic properties?) 75.10.Jm (Quantized spin models, including quantum spin frustration) 75.50.Lk (Spin glasses and other random magnets)

刘中强, 姜素蓉, 孔祥木. The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder[J]. 中国物理B, 2014, 23(8): 87505-087505.

Liu Zhong-Qiang (刘中强), Jiang Su-Rong (姜素蓉), Kong Xiang-Mu (孔祥木). The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder[J]. Chin. Phys. B, 2014, 23(8): 87505-087505.

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The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder

The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder

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