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The dynamics of one-dimensional random quantum Ising model with both nearest-neighbor and next-nearest-neighbor （NNN） interactions is investigated in the high temperature limit by the method of recurrence relations. Spin autocorrelations and the corresponding spectral densities of the system are calculated. Supposing that the exchange couplings （or the transverse fields） satisfy the double-Gaussian distribution, the effects of this distribution on the dynamics of the system is studied. The results show that the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one when the standard deviations σJ（or σB）of the random variables are small and there is no crossover when σJ（or σB）are large. Meanwhile, the effects of NNN interactions on the dynamics of the system are studied. It is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as Ki increase, especially when Ki>Ji/2（Ji and Ki are exchange couplings of the NN and NNN interactions, respectively）. However, the effects are small when the NNN interactions are weak （KiJi/2）.
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Keywords:
- random quantum Ising model /
- recurrence relations method /
- spin correlation function /
- spectral density
[1] ［1]Roldan J 1986 Physica A 136 255
[2] ［2]Niemeijer T 1967 Physica （Amsterdam） 36 377
[3] ［3]Katsura S, Horiguchi T, Suzuki M 1970 Physica （Utrecht） 46 67
[4] ［4]Binder K, Kob W 2005 Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics （Singapore: World Scientific）
[5] ［5]Plascak J A, Sá Barreto F C, Pires A S T， Goncalves L L 1983 J. Phys. C 16 49
[6] ［6]Watarai S, Matsubara T 1984 J. Phys. Soc. Jpn 53 3648
[7] ［7]Wu W, Ellman B, Rosenbaum T F, Aeppli G, Reich D H 1991 Phys. Rev. Lett. 67 2076
[8] ［8]Li J L, Lei S G 2008 Acta Phys. Sin. 57 5944 （in Chinese）［李嘉亮、类淑国 2008 物理学报 57 5944］
[9] ［9]Sen S, Hoff C N, Kuhl D E, McGrew D A 1996 Phys. Rev. B 53 3398
[10] ［10]Florencio J, de Alcantara Bonfim O F, Sá Barreto F C 1997 Physica A 235 523
[11] ［11]Qin J H, Xu S F, Fen S P 2006 Acta Phys. Sin. 55 5511 （in Chinese）［秦吉红、徐素芬、冯世平 2006 物理学报 55 5511］
[12] ［12]Florencio J, Sá Barreto F C 1999 Phy. Rev. B 60 9555
[13] ［13]Liu Z Q, Kong X M, Chen X S 2006 Phys. Rev. B 73 224412
[14] ［14]Xu L, Yan S L 2007 Acta Phys. Sin. 56 1691 （in Chinese）［许玲、晏世雷 2007 物理学报 56 1691］
[15] ［15]Nunes M E S, Florencio J 2003 Phys. Rev. B 68 014406
[16] ［16]Nunes M E S, Plascak J A, Florencio J 2004 Physica A 332 1
[17] ［17]Xu Z B, Kong X M, Liu Z Q 2008 Phys. Rev. B 77 184414
[18] ［18]Mezei F, Murani A P 1979 J. Magn. Magn. Mater 14 211
[19] ［19]Lee M H 1982 Phys. Rev. Lett. 49 1072
[20] ［20]Lee M H 1982 Phys. Rev. B 26 2547
[21] ［21]Lee M H 2000 Phys. Rev. E 62 1769
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[1] ［1]Roldan J 1986 Physica A 136 255
[2] ［2]Niemeijer T 1967 Physica （Amsterdam） 36 377
[3] ［3]Katsura S, Horiguchi T, Suzuki M 1970 Physica （Utrecht） 46 67
[4] ［4]Binder K, Kob W 2005 Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics （Singapore: World Scientific）
[5] ［5]Plascak J A, Sá Barreto F C, Pires A S T， Goncalves L L 1983 J. Phys. C 16 49
[6] ［6]Watarai S, Matsubara T 1984 J. Phys. Soc. Jpn 53 3648
[7] ［7]Wu W, Ellman B, Rosenbaum T F, Aeppli G, Reich D H 1991 Phys. Rev. Lett. 67 2076
[8] ［8]Li J L, Lei S G 2008 Acta Phys. Sin. 57 5944 （in Chinese）［李嘉亮、类淑国 2008 物理学报 57 5944］
[9] ［9]Sen S, Hoff C N, Kuhl D E, McGrew D A 1996 Phys. Rev. B 53 3398
[10] ［10]Florencio J, de Alcantara Bonfim O F, Sá Barreto F C 1997 Physica A 235 523
[11] ［11]Qin J H, Xu S F, Fen S P 2006 Acta Phys. Sin. 55 5511 （in Chinese）［秦吉红、徐素芬、冯世平 2006 物理学报 55 5511］
[12] ［12]Florencio J, Sá Barreto F C 1999 Phy. Rev. B 60 9555
[13] ［13]Liu Z Q, Kong X M, Chen X S 2006 Phys. Rev. B 73 224412
[14] ［14]Xu L, Yan S L 2007 Acta Phys. Sin. 56 1691 （in Chinese）［许玲、晏世雷 2007 物理学报 56 1691］
[15] ［15]Nunes M E S, Florencio J 2003 Phys. Rev. B 68 014406
[16] ［16]Nunes M E S, Plascak J A, Florencio J 2004 Physica A 332 1
[17] ［17]Xu Z B, Kong X M, Liu Z Q 2008 Phys. Rev. B 77 184414
[18] ［18]Mezei F, Murani A P 1979 J. Magn. Magn. Mater 14 211
[19] ［19]Lee M H 1982 Phys. Rev. Lett. 49 1072
[20] ［20]Lee M H 1982 Phys. Rev. B 26 2547
[21] ［21]Lee M H 2000 Phys. Rev. E 62 1769
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