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Communications in Mathematical Physics

Phase transitions in anisotropic lattice spin systems

Jürg Martin Fröhlich, Élliott H. Lieb

Published Oct 1, 1978• 128 citations
Publisher
DOI
10.1007/bf01612891

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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

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For pt.II see ibid., vol.14, p.1789 (1981). The phase transition of the anisotropic Ising lattices has been studied by the recently developed correlation reduction theory. The transition temperature and some other quantities at transition temperature for the anisotropic Ising lattices with spin 1 / 2 , 1, 3 / 2 are evaluated as functions of anisotropy parameter. The effect of anisotropy on these values is similar for the systems with three different spin values. Comparison with other calculations is made, and some physical significances are discussed.
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