二维无序铁磁系统临界性质的研究
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摘要
具有强磁性的铁磁体在温度高于居里温度时转变成磁性很弱的顺磁体，即为铁磁-顺磁二级相变。随着系统内禀场或外场的作用，系统居里温度会发生改变，呈现多种多样的相变特性。
单自旋铁磁系统的相变特性是本文的主要讨论内容。在本文中我们采用随机晶场作用下的键稀疏的Blume-Capel模型(BCM)和有随机晶场作用的键稀疏的横场伊辛模型，计算并讨论了以二维的蜂窝格子和平方格子为晶格点阵的系统的居里温度随着晶场、横场、键浓度和随机晶场浓度的变化关系。随机晶场作用的BCM中，居里温度随着晶场的增加而单调地递减，在晶场较大处出现三临界点，它连接着一级相变线和二级相变线。随着晶场随机浓度的减小，三临界点被抑制，同时出现了二级相变线的重入现象；当随机浓度很小的时候，系统在低温下始终处于有序状态，此时Blume-Capel模型相当于S=1／2的伊辛模型。对于两种不同的二维点阵，由于配位数的不同，也导致了相变特性的一些区别，特别在随机晶场条件下，得到了一些新的性质。键稀疏对系统临界性质的影响也是很明显的，尤其是对有序相的抑制作用十分显著。当横场被考虑在内，我们采用有随机晶场作用的BCM+TIM。横场也能有效降低系统相变温度，并能抑制三临界点和重入现象。如果在同一个系统中同时考虑横场和晶场，再加上晶场和交换相互作用的无序分布，那么这几个因素的相互竞争将会导致相变发生一些新的改变，我们得到了一个较复杂的铁磁自旋系统在各种条件下的相图和有意义的结果。
The ferromagnet shows strong magnetism in the condition of low temperature. But when the temperature reaches the Curie temperature the ferromagnet turns into paramagnet. It is the second-order phase transition from ferromagnet to paramagnet. With the effect of inner field and outer field, Curie temperature will decrease and the system will shows many kinds of properties of phase transition.
This article mainly discusses the critical properties of single spin (S=l) ferromagnetic system. In this article we introduce the bond-dilutied Blume-Capel model (BCM) with the random crystal field and combine the BCM as well as the transverse Ising model (TIM) with the random crystal field. The phase diagrams display the Curie temperature dependences of the crystal field, the transverse field, the bond concentration and the random crystal field concentration for the honeycomb lattice and the square lattice. In the BCM with random crystal field, the Curie temperature decreases monotonously with the increasing of the crystal field. The system with a larger crystal field can exhibit tricritical point at which the phase transition
changes from second to first order. When the random concentration of the crystal field decreases the tricritical point is depressed, at the same time the reentrant phenomenon occurs. The system will be ordered entirely when the random concentration is small enough at low temperatures. Due to the difference of coordination number, the honeycomb lattice and the square lattice display different transition properties. The bond dilution can depress the order phase effectively. When transverse field is introduced we adopt bond-diluted the MCM+TIM with random crystal field. The transverse field can also decrease the critical temperature. At the same time it can depress the tricritical point and the reentrant phenomenon. The competition between these factors shows some new critical features. We obtain a series of meaning results.
单自旋铁磁系统的相变特性是本文的主要讨论内容。在本文中我们采用随机晶场作用下的键稀疏的Blume-Capel模型(BCM)和有随机晶场作用的键稀疏的横场伊辛模型，计算并讨论了以二维的蜂窝格子和平方格子为晶格点阵的系统的居里温度随着晶场、横场、键浓度和随机晶场浓度的变化关系。随机晶场作用的BCM中，居里温度随着晶场的增加而单调地递减，在晶场较大处出现三临界点，它连接着一级相变线和二级相变线。随着晶场随机浓度的减小，三临界点被抑制，同时出现了二级相变线的重入现象；当随机浓度很小的时候，系统在低温下始终处于有序状态，此时Blume-Capel模型相当于S=1／2的伊辛模型。对于两种不同的二维点阵，由于配位数的不同，也导致了相变特性的一些区别，特别在随机晶场条件下，得到了一些新的性质。键稀疏对系统临界性质的影响也是很明显的，尤其是对有序相的抑制作用十分显著。当横场被考虑在内，我们采用有随机晶场作用的BCM+TIM。横场也能有效降低系统相变温度，并能抑制三临界点和重入现象。如果在同一个系统中同时考虑横场和晶场，再加上晶场和交换相互作用的无序分布，那么这几个因素的相互竞争将会导致相变发生一些新的改变，我们得到了一个较复杂的铁磁自旋系统在各种条件下的相图和有意义的结果。
The ferromagnet shows strong magnetism in the condition of low temperature. But when the temperature reaches the Curie temperature the ferromagnet turns into paramagnet. It is the second-order phase transition from ferromagnet to paramagnet. With the effect of inner field and outer field, Curie temperature will decrease and the system will shows many kinds of properties of phase transition.
This article mainly discusses the critical properties of single spin (S=l) ferromagnetic system. In this article we introduce the bond-dilutied Blume-Capel model (BCM) with the random crystal field and combine the BCM as well as the transverse Ising model (TIM) with the random crystal field. The phase diagrams display the Curie temperature dependences of the crystal field, the transverse field, the bond concentration and the random crystal field concentration for the honeycomb lattice and the square lattice. In the BCM with random crystal field, the Curie temperature decreases monotonously with the increasing of the crystal field. The system with a larger crystal field can exhibit tricritical point at which the phase transition
changes from second to first order. When the random concentration of the crystal field decreases the tricritical point is depressed, at the same time the reentrant phenomenon occurs. The system will be ordered entirely when the random concentration is small enough at low temperatures. Due to the difference of coordination number, the honeycomb lattice and the square lattice display different transition properties. The bond dilution can depress the order phase effectively. When transverse field is introduced we adopt bond-diluted the MCM+TIM with random crystal field. The transverse field can also decrease the critical temperature. At the same time it can depress the tricritical point and the reentrant phenomenon. The competition between these factors shows some new critical features. We obtain a series of meaning results.
引文
[1] 郭贻诚,《铁磁学》，人民教育出版社，1982．
[2] S. Honda, M. Nawate, M. Yoshima, IEEE Trans. Magn., 23 (1987) 2987
[3] T. Kaneyoshi, Physica A, 193 (2001) 200
[4] Y. E L Amraoui, H. Arhchoui and S.Sayouri, J. Mag. Mag. Mate. 219 (2000) 89．
[5] Y. ELAmraoui and A. Khmou, J Mag. Mag. Mate., 218 (2000) 182．
[6] T. Kaneyoshi, Physica A, 293 (2001) 200．
[7] K. H. Khoo and H. K. Sy, J. Phys: Condens. Matter, 13 (2001) 101．
[8] M. Barati and A. Ramazani, Phys. Rev. B, 62 (2000) 12130．
[9] C. Z. Yang and Z. Y. Li, Phys. Stat. Sol. (b) 146 (1988) 223．
[10] F. A. Granja, J. L. M. Lopez, J. Phys.: Condens. Matter, 5 (1993) A195．
[11] N. El Aouad, B. Laaboudi, M. Kerouad, and M. Saber, Phys. Rev. B 63 (2001) 054436-1．
[12] A. Aharony, Phys. Rev. B, 18 (1978) 3318．
[13] H. E. Borges and P. R. Silva, Physica A, 138 (1987) 561．
[14] M. Zukovic and T. Ldogaki, Phys. Rev. B, 61 (2000) 50．
[15] G. M. Zhang and C. Z. Yang, Phys. Rev. B, 48 (1993) 9452．
[16] A. Bobak and M. Jascur, Phys. Rev. B, 51 (1995) 11533．
[17] T. Kaneyoshi, J. Magn. Magn. Mate., 151 (1995) , 45．
[18] S. L. Yan and C. Z. Yang, Phys. Rev. B, 57 (1998) 3512．
[19] W. Stephan and B. W. Southern, Phys. Rev. B, 61 (2000) 11514．
[20] S. E. Kruger and J. Tichter, Phys. Rev. B, 61 (2000) 14607
[21] M. Blume, Phys. Rev. 141 (1966) 517．
[22] H.W. Capel, Physica 32 (1966) 966．
[23] A.E. Siqueira, L.P.Fittipaldi, Physica A 138 (1986) 592．
[24] T. Kaneyoshi, Physica A, 164 (1990) 730．
[25] N. Benayad, A. Bemupissef and N. Boccara, J. Phys. C 18 (1985) 1899．
[26] T. Kaneyoshi, J. Phys. C, 19 (1986) L557．
[27] S. A. Janiwsky, Phys. Lett. A, 134 (1988) 131．
[28] T. Kaneyoshi, Phys. Stat. Sol. (b) 170 (1992) 313．
[29] C. E. I. Carneiro, V. B. Henriques and S. R. Salinas, J Phys.: Condensed Matter, 1 (1989) 3687．
[30] D. P. Lara and J. A. Plascak, Physica A, 260 (1998) 443．
[31] K. Hui and A. N. Berker, Phys. Rev. Lett. 62 (1989) 2507．
[32] N. S. Branco and B.M. Boechat, Phys. Rev. B, 56 (1997) 11673．
[33] I. Puha and H. T. Diep, J. Mag. Mag. Mate. 224 (2001) 85．
[34] R. J. Elliott, G. A. Gehring, A. P. Malozemoff, S. R. P. Smith, N. S. Staude and R. N. Tyte, J. Phys. C, 4 (1971) L179．
[35] R. B. Srtinchcombe, J. Phys. C, 6 (1973) 2459．
[36] T. Kaneyoshi, Phys. Rev. B, 33 (1986) 526．
[37] E. F. Sarmento, R. B. Muniz and S. B. Cavalcanti, Phys. Rev. B, 36 (1987) 529．
[38] Z. Y. Li and Q. Jiang, Phys. Lett. A, 138 (1989) 247．
[39] J. L. Zhong, J. L. Li and C. Z. Yang, Phys. Stat. Sol. (b) 160 (1990) 329．
[40] Z. Y. Li, Phys. Rev. B, 42 (1990) 2597．
[41] S. L. Yan and C. Z. Yang, Sol. Stat. Commun., 100 (1996) 851．
[42] J. Rosenfeld and N. E. Ligherink, Phys. Rev. B, 62 (2000) 308．
[43] X. F. Jiang, J. L. Li, and J. L. Zhong and C. Z. Yang, Phys. Rev. B, 47 (1993) 827．
[44] X. F. Jiang, J. Magn. Magn. Mate., 134 (1994) 167．
[45] E. F. Sarmento and T. Kaneyoshi, Phys. Rev. B, 39 (1989) 9555．
[46] T. Kaneyoshi and Mielnicki, J. Phys.:Condens. Matter, 2 (1990) 8773．
[2] S. Honda, M. Nawate, M. Yoshima, IEEE Trans. Magn., 23 (1987) 2987
[3] T. Kaneyoshi, Physica A, 193 (2001) 200
[4] Y. E L Amraoui, H. Arhchoui and S.Sayouri, J. Mag. Mag. Mate. 219 (2000) 89．
[5] Y. ELAmraoui and A. Khmou, J Mag. Mag. Mate., 218 (2000) 182．
[6] T. Kaneyoshi, Physica A, 293 (2001) 200．
[7] K. H. Khoo and H. K. Sy, J. Phys: Condens. Matter, 13 (2001) 101．
[8] M. Barati and A. Ramazani, Phys. Rev. B, 62 (2000) 12130．
[9] C. Z. Yang and Z. Y. Li, Phys. Stat. Sol. (b) 146 (1988) 223．
[10] F. A. Granja, J. L. M. Lopez, J. Phys.: Condens. Matter, 5 (1993) A195．
[11] N. El Aouad, B. Laaboudi, M. Kerouad, and M. Saber, Phys. Rev. B 63 (2001) 054436-1．
[12] A. Aharony, Phys. Rev. B, 18 (1978) 3318．
[13] H. E. Borges and P. R. Silva, Physica A, 138 (1987) 561．
[14] M. Zukovic and T. Ldogaki, Phys. Rev. B, 61 (2000) 50．
[15] G. M. Zhang and C. Z. Yang, Phys. Rev. B, 48 (1993) 9452．
[16] A. Bobak and M. Jascur, Phys. Rev. B, 51 (1995) 11533．
[17] T. Kaneyoshi, J. Magn. Magn. Mate., 151 (1995) , 45．
[18] S. L. Yan and C. Z. Yang, Phys. Rev. B, 57 (1998) 3512．
[19] W. Stephan and B. W. Southern, Phys. Rev. B, 61 (2000) 11514．
[20] S. E. Kruger and J. Tichter, Phys. Rev. B, 61 (2000) 14607
[21] M. Blume, Phys. Rev. 141 (1966) 517．
[22] H.W. Capel, Physica 32 (1966) 966．
[23] A.E. Siqueira, L.P.Fittipaldi, Physica A 138 (1986) 592．
[24] T. Kaneyoshi, Physica A, 164 (1990) 730．
[25] N. Benayad, A. Bemupissef and N. Boccara, J. Phys. C 18 (1985) 1899．
[26] T. Kaneyoshi, J. Phys. C, 19 (1986) L557．
[27] S. A. Janiwsky, Phys. Lett. A, 134 (1988) 131．
[28] T. Kaneyoshi, Phys. Stat. Sol. (b) 170 (1992) 313．
[29] C. E. I. Carneiro, V. B. Henriques and S. R. Salinas, J Phys.: Condensed Matter, 1 (1989) 3687．
[30] D. P. Lara and J. A. Plascak, Physica A, 260 (1998) 443．
[31] K. Hui and A. N. Berker, Phys. Rev. Lett. 62 (1989) 2507．
[32] N. S. Branco and B.M. Boechat, Phys. Rev. B, 56 (1997) 11673．
[33] I. Puha and H. T. Diep, J. Mag. Mag. Mate. 224 (2001) 85．
[34] R. J. Elliott, G. A. Gehring, A. P. Malozemoff, S. R. P. Smith, N. S. Staude and R. N. Tyte, J. Phys. C, 4 (1971) L179．
[35] R. B. Srtinchcombe, J. Phys. C, 6 (1973) 2459．
[36] T. Kaneyoshi, Phys. Rev. B, 33 (1986) 526．
[37] E. F. Sarmento, R. B. Muniz and S. B. Cavalcanti, Phys. Rev. B, 36 (1987) 529．
[38] Z. Y. Li and Q. Jiang, Phys. Lett. A, 138 (1989) 247．
[39] J. L. Zhong, J. L. Li and C. Z. Yang, Phys. Stat. Sol. (b) 160 (1990) 329．
[40] Z. Y. Li, Phys. Rev. B, 42 (1990) 2597．
[41] S. L. Yan and C. Z. Yang, Sol. Stat. Commun., 100 (1996) 851．
[42] J. Rosenfeld and N. E. Ligherink, Phys. Rev. B, 62 (2000) 308．
[43] X. F. Jiang, J. L. Li, and J. L. Zhong and C. Z. Yang, Phys. Rev. B, 47 (1993) 827．
[44] X. F. Jiang, J. Magn. Magn. Mate., 134 (1994) 167．
[45] E. F. Sarmento and T. Kaneyoshi, Phys. Rev. B, 39 (1989) 9555．
[46] T. Kaneyoshi and Mielnicki, J. Phys.:Condens. Matter, 2 (1990) 8773．