中国物理B ›› 2003, Vol. 12 ›› Issue (3): 264-270.doi: 10.1088/1009-1963/12/3/304

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Critical slowing down of the Gaussian spin system on diamond-type hierarchical lattices

朱建阳1, 朱涵2   

  1. (1)Department of Physics, Beijing Normal University, Beijing 100875, China; (2)Department of Physics, Nanjing University, Nanjing 210093, China
  • 收稿日期:2002-08-21 修回日期:2002-10-19 出版日期:2003-03-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10075025).

Critical slowing down of the Gaussian spin system on diamond-type hierarchical lattices

Zhu Jian-Yang (朱建阳)a, Zhu Han (朱涵)b   

  1. a Department of Physics, Beijing Normal University, Beijing 100875, China; b Department of Physics, Nanjing University, Nanjing 210093, China
  • Received:2002-08-21 Revised:2002-10-19 Online:2003-03-16 Published:2005-03-16
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10075025).

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摘要： Based on the single-spin transition critical dynamics, we have investigated the critical slowing down of the Gaussian spin model situated on the fractal family of diamond-type hierarchical lattices. We calculate the dynamical critical exponent z and the correlation-length critical exponent ν using the dynamical decimation renormalization-group technique. The result, together with some earlier ones, suggests us to conclude that on a wide range of geometries, zν=1 is the general relationship, while the two exponents depend on the specific structure. However, we have investigated for various lattices in an earlier paper, the system studied in this paper shows highly universal z=1/ν=2 independent of the structure and the dimensionality.

Abstract: Based on the single-spin transition critical dynamics, we have investigated the critical slowing down of the Gaussian spin model situated on the fractal family of diamond-type hierarchical lattices. We calculate the dynamical critical exponent z and the correlation-length critical exponent $\nu$ using the dynamical decimation renormalization-group technique. The result, together with some earlier ones, suggests us to conclude that on a wide range of geometries, z$\nu$=1 is the general relationship, while the two exponents depend on the specific structure. However, we have investigated for various lattices in an earlier paper, the system studied in this paper shows highly universal z=1/$\nu$=2 independent of the structure and the dimensionality.

Key words: nonequilibrium thermodynamics and irreversible processes, dynamical critical phenomena, dynamical real-space renormalization-group

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
05.45.Df (Fractals) 05.70.Jk (Critical point phenomena) 05.70.Ln (Nonequilibrium and irreversible thermodynamics) 02.20.-a (Group theory)