Sierpienski垫片上各向异性伊辛模型的Phase diagram和奇异自旋-自旋关联
Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket
摘要：
对分形Sierpienski垫片上的各向异性反铁磁伊辛模型进行了深入研究，揭示了其奇异性质.得到了系统在磁场-相互作用平面内的基态相图.三个平台相的热力学性质进行了探讨，探索的磁化强度，比热，磁化率和自旋自旋相关的温度依赖性。在这个模型中没有观察到相变。在没有磁场的情况下，用$0 \leq$ J $_b/$ J $_a<1$得到了自旋关联长度的温度依赖性，并揭示了在J $_b/$ J $_a=1$处不同相之间的有趣交叉行为，其动力学可以用比热、磁化率和自旋关联函数的J $_b/$ J $_a$依赖性来描述.在$1/3$平台无序相和$5/9$平台部分有序亚铁磁相中都得到了与Sierpienski垫片具有相同特殊旋转对称性的奇异自旋-自旋关联图样.此外，一个量子方案制定的分形Sierpienski垫片与海森堡相互作用的热力学研究。我们发现，不寻常的相关长度的温度依赖性保持完整的一个小的量子涨落。
英文摘要：
The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with $0 \leq$J$_b/$J$_a<1$, and an interesting crossover behavior between different phases at J$_b/$J$_a=1$ is unveiled, whose dynamics can be described by the J$_b/$J$_a$-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the $1/3$ plateau disordered phase and the $5/9$ plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.
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