具有三重态相互作用的混合自旋伊辛模型在米字格上的强和弱普适临界行为
Strong- and weak-universal critical behaviour of a mixed-spin Ising model with triplet interactions on the Union Jack (centered square) lattice
摘要：
通过建立严格的映射等价关系，精确求解了具有四种不同三重自旋相互作用和单轴单离子各向异性的米字格点上自旋1/2和自旋S混合伊辛模型与对偶正方形格点上零场（对称）八顶点模型.上述精确映射等价性的严格证明由两种独立的方法提供，这两种方法利用零场八顶点模型的图论表示或自旋表示。的相互作用的各向异性以及单轴单离子各向异性的相变和临界现象的影响，特别是检查。结果表明，所考虑的模型具有较强的普遍的临界行为与恒定的临界指数时，考虑各向同性模型与四个相等的三重态相互作用或各向异性模型与一个三重态相互作用不同于其他三个。具有两种不同的三重态相互作用的各向异性模型，这是成对彼此相等，相反，表现出弱的普遍的临界行为与临界指数连续变化的相对强度的三重态相互作用以及单轴单离子各向异性。证明了自旋为整数值的混合自旋伊辛模型的临界指数的变化与自旋为半奇数值的混合自旋模型的临界指数的变化基本不同。
英文摘要：
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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