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With a real-space renormalization-group method, the anisotropic quantum Heisenberg model on three-dimensional diamond-type hierarchical lattice is studied, and the phase diagram and critical properties are obtained. For the ferromagnetic system, it is shown that there is a finite-temperature phase transition for Δ=0 where Δ is the anisotropy parameter. The order parameter and critical exponents are also calculated. For the antiferromagnetic model, we find that the critical temperature is not equal to zero for Δ=0 and there is not reentrant behavior on the critical line.
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Keywords:
- phase diagram /
- Heisenberg model /
- diamond-type hierarchical lattice /
- renormalization-group method
[1] Boyarchenkov A S, Ovchinnikov A S, Bostrem I G, Baranov N V, Hosokoshi Y, Inoue K 2005 J. Phys.: Condens. Matt. 17 1769
[2] Albuquerque A F, Troyer M, Oitmaa J 2008 Phys. Rev. B 78 132402
[3] Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 531(in Chinese)[张松俊、蒋建军、刘拥军 2008 57 531]
[4] Cai Z, Lu W B, Liu Y J 2008 Acta Phys. Sin. 57 7267(in Chinese)[蔡 卓、陆文彬、刘拥军 2008 57 7267]
[5] Qin M, Tian D P, Tao Y J 2008 Acta Phys. Sin. 57 5395(in Chinese)[秦 猛、田东平、陶应娟 2008 57 5395]
[6] Berker A N, Ostlund S 1979 J. Phys. C: Solid State Phys. 12 4961
[7] Caride A O, Tsallis C, Zanette S 1983 Phys. Rev. Lett. 51 145
[8] Sousa J R, Branco N S, Boechat B, Cordeiro C 2003 Phys. A 328 167
[9] Chame A 1991 J. Phys. : Condens. Matt. 3 9115
[10] Souza A M 1993 Phys. Rev. B 48 3744
[11] Branco N S, Sousa J R 2000 Phys. Rev. B 62 5742
[12] Mariz A M, Santos R M, Tsallis C, Santos R R 1985 J. Phys. Lett. A 108 95
[13] Suzuki M, Takano H 1979 Phys. Lett. A 69 426
[14] Takano H, Suzuki M 1981 J. Stat. Phys. 26 635
[15] Plascak J A 1984 J. Phys. A: Math. Gen. 17 597
[16] Kong X M, Lin Z Q, Zhu J Y 2000 Sci. Chin. Ser. A 30 661(in Chinese)[孔祥木、林振全、朱建阳 2000 中国科学,A辑 30 661]
[17] Li Y, Kong X M, Huang J Y 2002 Acta Phys. Sin. 51 1346 (in Chinese) [李 英、孔祥木、黄家寅 2002 51 1346]
[18] Liu J, Kong X M, Li Y P, Huang J Y 2004 Acta Phys. Sin. 53 2275(in Chinese) [刘 杰、孔祥木、李永平、黄家寅 2004 53 2275]
[19] Yin X C, Yin H, Kong X M 2006 Acta Phys. Sin. 55 4901(in Chinese)[尹训昌、尹 慧、孔祥木 2006 55 4901]
[20] Sousa J R, Boechat B, Cordeiro C, Branco N S 2005 Phys. Rev. E 71 016135
[21] Branco N S, Sousa J R, Ghosh A 2008 Phys. Rev. E 77 031129
[22] Mariz A M, Tsallis C, Caride A O 1985 J. Phys. C: Solid State Phys. 18 4189
[23] Stinchcombe R B 1981 J. Phys. C: Solid State Phys. 14 397
[24] Yang Z R 1988 Phys. Rev. B 38 728
[25] Cassi D 1992 Phys. Rve. Lett. 68 3631
[26] Cassi D 1996 Phys. Rve. Lett. 76 2941
[27] Caride A O, Tsallis C 1987 J. Phys. A: Math. Gen. 20 665
[28] Continentino M A, Mello E V 1990 J. Phys. :Condens. Matter 2 3131
[29] Qin Y, Yang Z R 1991 Phys. Rev. B 43 8576
[30] Yang Z R 1996 Fractal Physics (Shanghai:Shanghai Scientific and Technological Education Publishing House) 83—88 (in Chinese)[杨展如 1996 分形物理学(上海:上海科技教育出版社)第83—88页]
[31] Sousa J R, Plascak J A 1997 J. Phys. Lett. A 237 66
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[1] Boyarchenkov A S, Ovchinnikov A S, Bostrem I G, Baranov N V, Hosokoshi Y, Inoue K 2005 J. Phys.: Condens. Matt. 17 1769
[2] Albuquerque A F, Troyer M, Oitmaa J 2008 Phys. Rev. B 78 132402
[3] Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 531(in Chinese)[张松俊、蒋建军、刘拥军 2008 57 531]
[4] Cai Z, Lu W B, Liu Y J 2008 Acta Phys. Sin. 57 7267(in Chinese)[蔡 卓、陆文彬、刘拥军 2008 57 7267]
[5] Qin M, Tian D P, Tao Y J 2008 Acta Phys. Sin. 57 5395(in Chinese)[秦 猛、田东平、陶应娟 2008 57 5395]
[6] Berker A N, Ostlund S 1979 J. Phys. C: Solid State Phys. 12 4961
[7] Caride A O, Tsallis C, Zanette S 1983 Phys. Rev. Lett. 51 145
[8] Sousa J R, Branco N S, Boechat B, Cordeiro C 2003 Phys. A 328 167
[9] Chame A 1991 J. Phys. : Condens. Matt. 3 9115
[10] Souza A M 1993 Phys. Rev. B 48 3744
[11] Branco N S, Sousa J R 2000 Phys. Rev. B 62 5742
[12] Mariz A M, Santos R M, Tsallis C, Santos R R 1985 J. Phys. Lett. A 108 95
[13] Suzuki M, Takano H 1979 Phys. Lett. A 69 426
[14] Takano H, Suzuki M 1981 J. Stat. Phys. 26 635
[15] Plascak J A 1984 J. Phys. A: Math. Gen. 17 597
[16] Kong X M, Lin Z Q, Zhu J Y 2000 Sci. Chin. Ser. A 30 661(in Chinese)[孔祥木、林振全、朱建阳 2000 中国科学,A辑 30 661]
[17] Li Y, Kong X M, Huang J Y 2002 Acta Phys. Sin. 51 1346 (in Chinese) [李 英、孔祥木、黄家寅 2002 51 1346]
[18] Liu J, Kong X M, Li Y P, Huang J Y 2004 Acta Phys. Sin. 53 2275(in Chinese) [刘 杰、孔祥木、李永平、黄家寅 2004 53 2275]
[19] Yin X C, Yin H, Kong X M 2006 Acta Phys. Sin. 55 4901(in Chinese)[尹训昌、尹 慧、孔祥木 2006 55 4901]
[20] Sousa J R, Boechat B, Cordeiro C, Branco N S 2005 Phys. Rev. E 71 016135
[21] Branco N S, Sousa J R, Ghosh A 2008 Phys. Rev. E 77 031129
[22] Mariz A M, Tsallis C, Caride A O 1985 J. Phys. C: Solid State Phys. 18 4189
[23] Stinchcombe R B 1981 J. Phys. C: Solid State Phys. 14 397
[24] Yang Z R 1988 Phys. Rev. B 38 728
[25] Cassi D 1992 Phys. Rve. Lett. 68 3631
[26] Cassi D 1996 Phys. Rve. Lett. 76 2941
[27] Caride A O, Tsallis C 1987 J. Phys. A: Math. Gen. 20 665
[28] Continentino M A, Mello E V 1990 J. Phys. :Condens. Matter 2 3131
[29] Qin Y, Yang Z R 1991 Phys. Rev. B 43 8576
[30] Yang Z R 1996 Fractal Physics (Shanghai:Shanghai Scientific and Technological Education Publishing House) 83—88 (in Chinese)[杨展如 1996 分形物理学(上海:上海科技教育出版社)第83—88页]
[31] Sousa J R, Plascak J A 1997 J. Phys. Lett. A 237 66
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