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通过键移动重整化群的方法, 分析了Sierpinski 地毯上S4模型的临界行为, 得到了系统的临界点. 由得到的结果可知, 本系统不仅有一个高斯不动点, 而且还存在着一个Wilson Fisher不动点, 把它与Sierpinski 地毯上的高斯模型相互对比, 发现本系统的临界点变化很大. 这说明这两个系统隶属于两个不同的普适类.
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关键词:
- Sierpinski 地毯 /
- S4模型 /
- 重整化群
According to the bond-moving renormalization group technique, the critical behaviour of S4 model for Sierpinski carpet is investigated, then the critical points are obtained. From the results we find that there are a Wilson-Fisher fixed point and a Gaussian fixed point. In contrast to the Gauss model for Sierpinski carpet, the critical points have altered obviously. Results indicate that the two systems belong to two different universal classes.-
Keywords:
- Sierpinski carpet /
- S4model /
- renormalization group
[1] Gefen Y, Mandelbrot B, Aharony A 1980 Phys .Rev. Lett. 45 855
[2] Gefen Y, Aharony A, Mandelbrot B 1983 J. Phys. A 16 1267
[3] Gefen Y, Aharony A, Mandelbrot B 1984 J. Phys. A 17 435
[4] Gefen Y, Aharony A, Mandelbrot B 1984 J. Phy. A 17 1277
[5] Hu B 1985 Phys. Rev. Lett. 55 2316
[6] Wang Z D, Gong C D, Arno H 1986 Phys. Rev. A 34 1531
[7] Wu Y K, Hu B 1987 Phys. Rev. A 35 1404
[8] Fahnle M, Braun P 1988 Phys. Rev. B 38 7094
[9] Yang Z R 1988 Phys. Rev. B 38 728
[10] Kong X M, Li S 2000 Commun. Theor. Phys. 33 63
[11] Lin Z Q, Kong X M 2001 Chin. Phys. Lett. 18 882
[12] Zhu J Y, Zhu H 2003 Chin. Phys. 12 264
[13] Sun C F 2005 Acta Phys. Sin. 54 3768 (in Chinese) [孙春峰 2005 54 3768]
[14] Li Y, Kong X M 2005 Physica A 356 589
[15] 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]
[16] Chen X, Zhang J S 2014 Chin. Phys. B 23 096401
[17] Ma Y B, Zhang H W, Li Y X 2014 Acta Phys. Sin. 63 118102 (in Chinese) [马岩冰, 张怀武, 李元勋 2014 63 118102]
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[1] Gefen Y, Mandelbrot B, Aharony A 1980 Phys .Rev. Lett. 45 855
[2] Gefen Y, Aharony A, Mandelbrot B 1983 J. Phys. A 16 1267
[3] Gefen Y, Aharony A, Mandelbrot B 1984 J. Phys. A 17 435
[4] Gefen Y, Aharony A, Mandelbrot B 1984 J. Phy. A 17 1277
[5] Hu B 1985 Phys. Rev. Lett. 55 2316
[6] Wang Z D, Gong C D, Arno H 1986 Phys. Rev. A 34 1531
[7] Wu Y K, Hu B 1987 Phys. Rev. A 35 1404
[8] Fahnle M, Braun P 1988 Phys. Rev. B 38 7094
[9] Yang Z R 1988 Phys. Rev. B 38 728
[10] Kong X M, Li S 2000 Commun. Theor. Phys. 33 63
[11] Lin Z Q, Kong X M 2001 Chin. Phys. Lett. 18 882
[12] Zhu J Y, Zhu H 2003 Chin. Phys. 12 264
[13] Sun C F 2005 Acta Phys. Sin. 54 3768 (in Chinese) [孙春峰 2005 54 3768]
[14] Li Y, Kong X M 2005 Physica A 356 589
[15] 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]
[16] Chen X, Zhang J S 2014 Chin. Phys. B 23 096401
[17] Ma Y B, Zhang H W, Li Y X 2014 Acta Phys. Sin. 63 118102 (in Chinese) [马岩冰, 张怀武, 李元勋 2014 63 118102]
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