Please wait a minute...
Chin. Phys. B, 2014, Vol. 23(8): 087505    DOI: 10.1088/1674-1056/23/8/087505
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

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
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 σJ (or σB) of the exchange couplings Ji (or the random transverse fields Bi) 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 σJ (or σB) 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 σJ or a disordered behavior for large σB. In this instance, SAFs exhibit a similar long-time tail, i.e., C(t)~ t-2 for large t. Similar properties are obtained when Ji (or Bi) 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.
Keywords:  random transverse Ising model      spin autocorrelation function      spectral density      long-time tail  
Received:  03 January 2014      Revised:  26 March 2014      Accepted manuscript online: 
PACS:  75.10.Pq (Spin chain models)  
  75.40.Gb (Dynamic properties?)  
  75.10.Jm (Quantized spin models, including quantum spin frustration)  
  75.50.Lk (Spin glasses and other random magnets)  
Fund: 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).
Corresponding Authors:  Liu Zhong-Qiang     E-mail:  phyzhqliu@163.com

Cite this article: 

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 2014 Chin. Phys. B 23 087505

[1] Vaidya H G and Tracy C A 1978 Physica A 92 1
[2] McCoy B M, Perk J H H and Shrock R E 1983 Nucl. Phys. B 220 269
[3] Müller G and Shrock R E 1984 Phys. Rev. B 29 288
[4] Its A R, Izergin A G, Korepin V E and Slavnov N A 1993 Phys. Rev. Lett. 70 1704
[5] Stolze J, Nőppert A and Müller G 1995 Phys. Rev. B 52 4319
[6] Sur A, Jasnow D and Lowe I J 1975 Phys. Rev. B 12 3845
[7] Brandt U and Jacoby K 1976 Z. Phys. B 25 181
[8] Capel H W and Perk J H H 1977 Physica A 87 211
[9] Florencio J Jr and Lee M H 1987 Phys. Rev. B 35 1835
[10] Niemeijer T 1967 Physica 36 377
[11] Katsura S, Horiguchi T and Suzuki M 1970 Physica 46 67
[12] Dekeyser R and Lee M H 1991 Phys. Rev. B 43 8131
[13] Rieger H and Iglói F 1997 Europhys. Lett. 39 135
[14] Young A P 1997 Phys. Rev. B 56 11691
[15] Florencio J and Sá Barreto F C 1999 Phys. Rev. B 60 9555
[16] Liu Z Q, Kong X M and Chen X S 2006 Phys. Rev. B 73 224412
[17] Boechat B, Cordeiro C, Florencio J, Sá Barreto F C and de Alcantara Bonfim O F 2000 Phys. Rev. B 61 14327
[18] Boechat B, Cordeiro C, de Alcantara Bonfim O F, Florencio J and Sá Barreto F C 2000 Braz. J. Phys. 30 693
[19] Chen S X, Shen Y Y and Kong X M 2010 Phys. Rev. B 82 174404
[20] Jia X and Chakravarty S 2006 Phys. Rev. B 74 172414
[21] Nunes M E S and Florencio J 2003 Phys. Rev. B 68 014406
[22] Nunes M E S, Plascak J A and Florencio J 2004 Physica A 332 1
[23] Xu Z B, Kong X M and Liu Z Q 2008 Phys. Rev. B 77 184414
[24] Li Y F and Kong X M 2013 Chin. Phys. B 22 037502
[25] Laflorencie N, Rieger H, Sandvik A W and Henelius P 2004 Phys. Rev. B 70 054430
[26] Li Y F, Shen Y Y and Kong X M 2012 Acta Phys. Sin. 61 107501 (in Chinese)
[27] Sen S and Blersch T D 1998 Physica A 253 178
[28] Plascak J A, Pires A S T and Sá Barreto F C 1982 Solid State Commun. 44 787
[29] Plascak J A, Sá Barreto F C, Pires A S T and Goncalves L L 1983 J. Phys. C 16 49
[30] Watarai S and Matsubara T 1984 J. Phys. Soc. Jpn. 53 3648
[31] Levitsky R R, Zachek I R, Mits E V, Grigas J and Paprotny W 1986 Ferroelectrics 67 109
[32] Wu W, Ellman B, Rosenbaum T F, Aeppli G and Reich D H 1991 Phys. Rev. Lett. 67 2076
[33] Rønow H M, Parthasarathy R, Jensen J, Aeppli G, Rosenbaum T F and McMorrow D F 2005 Science 308 389
[34] Viswanath V S and Müller G 1994 The Recursion Method – Applications to Many-Body Dynamics (Berlin: Springe-Verlag Press)
[35] Florencio J Jr and Lee M H 1985 Phys. Rev. A 31 3231
[36] Lee M H 1982 Phys. Rev. Lett. 49 1072
[37] Lee M H 1982 Phys. Rev. B 26 2547
[38] Lee M H 1983 J. Math. Phys. 24 2512
[39] Hong J and Lee M H 1993 Phys. Rev. Lett. 70 1972
[40] Mori H 1965 Prog. Theor. Phys. 34 399
[41] Sen S, Mahanti S D and Cai Z X 1991 Phys. Rev. B 43 10990
[42] Sen S 1995 Physica A 222 195
[43] Sen S 1993 Proc. R. Soc. London A 441 169
[44] Florencio J, de Alcantara Bonfim O F and Sá Barreto F C 1997 Physica A 235 523
[45] Hong J and Kee H Y 1995 Phys. Rev. B 52 2415
[46] Kee H Y and Hong J 1997 Phys. Rev. B 55 5670
[47] Stolze J, Viswanath V S and Müller G 1992 Z. Phys. B 89 45
[48] Böhm M, Leschke H, Henneke M, Viswanath V S, Stolze J and Müller G 1994 Phys. Rev. B 49 417
[1] A robust power spectrum split cancellation-based spectrum sensing method for cognitive radio systems
Qi Pei-Han (齐佩汉), Li Zan (李赞), Si Jiang-Bo (司江勃), Gao Rui (高锐). Chin. Phys. B, 2014, 23(12): 128401.
[2] Dynamics of one-dimensional random quantum XY system with Dzyaloshinskii–Moriya interaction
Li Yin-Fang (李银芳), Kong Xiang-Mu (孔祥木). Chin. Phys. B, 2013, 22(3): 037502.
[3] Quantum correlation dynamics of three non-coupled two-level atoms in different reservoirs
Wang Xiao-Yun (王小云), Ding Bang-Fu (丁邦福), Zhao He-Ping (赵鹤平). Chin. Phys. B, 2013, 22(2): 020309.
[4] Scattering of scalar light wave from a Gaussianben–Schell model medium
Wang Tao(王涛) and Zhao Dao-Mu(赵道木). Chin. Phys. B, 2010, 19(8): 084201.
No Suggested Reading articles found!