Journal of Jilin University(Science Edition)

Critical Properties of the S~4 Model on a Type of Hierarchical Lattice

YU Chun-ri

Published Jan 1, 2009• 0 citations

Abstract

Using the renormalization-group transformation method together with the cumulative expansion technique,the phase transition and critical properties of the S4 model on a type of hierarchical lattice were studied,and its fixed points and critical exponents were obtained.The results show that there exists a Wilson-Fisher fixed point besides the Gaussian fixed point,compared with those of the S4 model on the special diamond-type of hierarchical lattices,the critical points and critical exponents have changed.It has been found that both of them belong to different university classes.

Related papers

Critical properties of the S4 model on a special diamond-type hierarchical lattice

Xun-Chang Yin, Yin Hui, Xiang-Mu Kong +1 more

Using the renormalization-group transformation and cumulative expansion technique, the phase transition and critical properties of the S4 model on a special diamond-type hierarchical lattice are studied, and its fixed points and critical exponents are obtained. The results show that there exists a Wilson-Fisher fixed point besides the Gaussian fixed point, and compared with the Gaussian model of the special diamond-type hierarchical lattices, the critical exponents have changed.

Acta Physica SinicaJan 1, 20064 citations

Phase transition of the S4 model on diamond lattice

YIN Xun-Chang, Wanfang Liu, ZHU Zu-Song +3 more

According to the real space renormalization group method, the phase transition of S4 model on a diamond lattice is studied, and its critical points are obtained. The results show that there only exist a Gaussian fixed point and the Wilson-Fisher fixed point is not found. Compared to the Gauss model on a diamond lattice, they have the same critical points. The results indicate that the two systems belong to the same university class.

Jan 1, 20180 citations

Renormalization Group of the Gauss Model on a Type of Hierarchical Lattice

Zhu Zu-song

Gauss mode is allowed to take a continuous spin value,so the study of Gauss mode is of great value to understand better the critical properties of ferromagnets.In this paper,using the renormalization-group transformation technique,the phase transition and critical properties of the modified Gauss model on a type of hierarchical lattice are studied,and its fixed points is K=b33 obtained.In terms of the RG transformation and scaling theory,critical exponents α=0.758 and v=0.414 are obtained.

Journal of Anqing Teachers CollegeJan 1, 20080 citations

Phase transitions of the anisotropic Ashkin-Teller model on a family of diamond-type hierarchical lattices

Le Jian-Xin, Zhao‐Di Yang

The phase transitions of the anisotropic Ashkin-Teller model on a family of diamond-type hierarchical lattices is studied by means of the transfer-matrix method and the real-space renormalization-group transformation. We find that the phase diagram, for the ferromagnetic case, consists of five phases, i.e., the fully disordered paramagnetic phase P, the fully ordered ferromagnetic phase F, and three partially ordered ferromagnetic phases F(s), F(sigma), and F(s sigma), as well as ten nontrivial fixed points. The correlation length critical exponents and the crossover exponents are also calculated. In addition, we also investigate the variations of the critical exponents with the fractal dimension d(f), the number of branches m, and the number of bonds per branch b of the generator of the family of diamond-type hierarchical lattices. Finally we give a brief discussion about universality.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsDec 17, 20038 citations

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

朱建阳, 朱涵

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 v 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,zv=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/v=2 independent of the structure and the dimensionality.

中国物理B：英文版Mar 16, 20050 citations

Critical behavior of the quantum Heisenberg model on three-dimensional diamond-type hierarchical lattice

Zou Wei-Ke, Xiang-Mu Kong, Chun-Yang Wang +1 more

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.

Acta Physica SinicaJan 1, 20102 citations