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Phase transition of the S4 model on diamond lattice

YIN Xun-Chang, Wanfang Liu, ZHU Zu-Song, MA Ye-Wan, WEN Jun, ZHANG Li-Hua

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
In this paper, the phase diagrams and the critical behavior of the spin-1/2 anisotropic XXZ ferromagnetic model (the anisotropic parameter Δ\in(-\infty,1]) on two kinds of diamond-type hierarchical (DH) lattices with fractal dimensions d_{f}=2.58 and 3, respectively, are studied via the real-space renormalization group method. It is found that in the isotropic Heisenberg limit (Δ=0), there exist finite temperature phase transitions for the two kinds of DH lattices above. The systems are also investigated in the range of -\infty