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Using equivalent transformation and spin-rescaling methods, the Gauss model on a decorated square lattice is studied. It is found that the square decorated Gauss lattice could be transformed into a regular square Gauss lattice with nearest-neighbor, and next-nearest-neighbor interactions. By calculating the regular square-lattice Gauss model, the critical temperature of the Gauss model is obtained on a decorated square lattice, and the exact phase diagram of this system can also be obtained.
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Keywords:
- decorated square lattice /
- Gauss model /
- equivalent transformation /
- phase diagram
[1] Ma S K 1976 Modern Theory of Critical Phenomena (London: Benjamin)
[2] [3] [4] Goldenfeld N 1992 Lectures on Phase Transitions and the Renormalization Group (Massachusetts: Addison-Wesley)
[5] Cardy J 1998 Scaling and Renormalization in Statistical Physics (London: Cambridge University)
[6] [7] Stanley H E 1999 Rev. Mod. Phys. 71 5358
[8] [9] [10] Yang Z R 1996 Fractal Physics (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [杨展如 1996 分形物理学 (上海: 上海科技教育出版社)]
[11] [12] Li S, Yang Z R 1997 Phys. Rev. E 55 6656
[13] [14] Zhu J Y, Yang Z R 1999 Phys. Rev. E 59 1551
[15] [16] Kong X M, Yang Z R 2004 Phys. Rev. E 69 016101
[17] Sun C F 2005 Acta Phys. Sin. 54 3768 ( in Chinese) [孙春峰 2005 物理学报 54 3768]
[18] [19] [20] 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 物理学报 55 4901]
[21] [22] Li Y, Kong X M, Huang J Y 2002 Acta Phys. Sin. 51 1364 (in Chinese) [李英, 孔祥木, 黄家寅 2002 物理学报 51 1364]
[23] 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 物理学报 53 2275]
[24] [25] Kong X M, Lin Z Q, Zhu J Y 2000 Sci. Chin. A 30 661 (in Chinese) [孔祥木, 林振权, 朱建阳 2000 中国科学A 30 661]
[26] [27] [28] Lin Z Q, Kong X M 2001 Chin. Phys. Lett. 18 882
[29] [30] Zou W K, Kong X M, Wang C Y, Gao Z Y 2010 Acta Phys. Sin. 59 4874 (in Chinese) [邹维科, 孔祥木, 王春阳, 高中扬 2010 物理学报 59 4874]
[31] [32] Onsager L 1944 Phys. Rev. 65 117
[33] [34] Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (New York: Academic)
[35] [36] 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 物理学报 57 531]
[37] Lackova L, Horiguchi T 2003 Physica A 319 311
[38] [39] [40] Wang C Y, Kong X M 2005 Acta Phys. Sin. 54 4365 (in Chinese) [王春阳, 孔祥木 2005 物理学报 54 4365]
[41] [42] Sun C F, Kong X M, Yin X C 2006 Commun. Theor. Phys. 45 555
[43] [44] Strecka J, Jascur M 2002 Phys. Rev. B 66 174415
[45] Strecka J, Jascur M 2003 J. Magn. Magn. Mater. 260 415
[46] [47] Berlin T H, Kac M 1952 Phys. Rev. 86 821
[48] [49] [50] Hu B 1982 Phys. Rep. 91 233
[51] Yang Z R 2007 Quantum Statistical Physics (Beijing: Higher Education Press) pp298, 299, 313 (in Chinese) [杨展如 2007 量子统计物理学 (北京: 高等教育出版社)第298, 299, 313页]
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[1] Ma S K 1976 Modern Theory of Critical Phenomena (London: Benjamin)
[2] [3] [4] Goldenfeld N 1992 Lectures on Phase Transitions and the Renormalization Group (Massachusetts: Addison-Wesley)
[5] Cardy J 1998 Scaling and Renormalization in Statistical Physics (London: Cambridge University)
[6] [7] Stanley H E 1999 Rev. Mod. Phys. 71 5358
[8] [9] [10] Yang Z R 1996 Fractal Physics (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [杨展如 1996 分形物理学 (上海: 上海科技教育出版社)]
[11] [12] Li S, Yang Z R 1997 Phys. Rev. E 55 6656
[13] [14] Zhu J Y, Yang Z R 1999 Phys. Rev. E 59 1551
[15] [16] Kong X M, Yang Z R 2004 Phys. Rev. E 69 016101
[17] Sun C F 2005 Acta Phys. Sin. 54 3768 ( in Chinese) [孙春峰 2005 物理学报 54 3768]
[18] [19] [20] 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 物理学报 55 4901]
[21] [22] Li Y, Kong X M, Huang J Y 2002 Acta Phys. Sin. 51 1364 (in Chinese) [李英, 孔祥木, 黄家寅 2002 物理学报 51 1364]
[23] 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 物理学报 53 2275]
[24] [25] Kong X M, Lin Z Q, Zhu J Y 2000 Sci. Chin. A 30 661 (in Chinese) [孔祥木, 林振权, 朱建阳 2000 中国科学A 30 661]
[26] [27] [28] Lin Z Q, Kong X M 2001 Chin. Phys. Lett. 18 882
[29] [30] Zou W K, Kong X M, Wang C Y, Gao Z Y 2010 Acta Phys. Sin. 59 4874 (in Chinese) [邹维科, 孔祥木, 王春阳, 高中扬 2010 物理学报 59 4874]
[31] [32] Onsager L 1944 Phys. Rev. 65 117
[33] [34] Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (New York: Academic)
[35] [36] 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 物理学报 57 531]
[37] Lackova L, Horiguchi T 2003 Physica A 319 311
[38] [39] [40] Wang C Y, Kong X M 2005 Acta Phys. Sin. 54 4365 (in Chinese) [王春阳, 孔祥木 2005 物理学报 54 4365]
[41] [42] Sun C F, Kong X M, Yin X C 2006 Commun. Theor. Phys. 45 555
[43] [44] Strecka J, Jascur M 2002 Phys. Rev. B 66 174415
[45] Strecka J, Jascur M 2003 J. Magn. Magn. Mater. 260 415
[46] [47] Berlin T H, Kac M 1952 Phys. Rev. 86 821
[48] [49] [50] Hu B 1982 Phys. Rep. 91 233
[51] Yang Z R 2007 Quantum Statistical Physics (Beijing: Higher Education Press) pp298, 299, 313 (in Chinese) [杨展如 2007 量子统计物理学 (北京: 高等教育出版社)第298, 299, 313页]
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