Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice.
Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice.
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DOI：
10.3390/e20020091
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发表时间：
2018-01-29
期刊：
影响因子：
--
通讯作者：
Strečka J
中科院分区：
文献类型：
--
作者：
Strečka J
通过建立与对偶方晶格上相应的零场(对称)八顶点模型的严格映射等价，精确地求解了具有四种不同三自旋(三重态)相互作用和单轴单离子各向异性的Union Jack(中心正方形)晶格上的混合自旋1/2和自旋-S伊辛模型.利用零场八顶点模型的图论表示或自旋表示的两种独立方法提供了上述精确映射等价性的严格证明。特别研究了相互作用各向异性和单轴单离子各向异性对相变和临界现象的影响。结果表明，当考虑具有四个相等三重态相互作用的各向同性模型或具有不同于其他三个三重态相互作用的各向异性模型时，所考虑的模型呈现出具有恒定临界指数的强普适临界行为。相反，具有两个相互相等的不同三重态相互作用的各向异性模型呈现弱-普适临界行为，临界指数随三重态相互作用的相对强度以及单轴单离子各向异性而连续变化。结果表明，混合自旋伊辛模型的临界指数随S自旋整值的变化与半奇整数自旋S的对应模型基本不同。
The mixed spin-1/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S.
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