Strečka Jozef
Department of Theoretical Physics and Astrophysics, Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovak Republic.
Entropy (Basel). 2018 Jan 29;20(2):91. doi: 10.3390/e20020091.
The mixed spin-1/2 and spin- 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 differ basically from their counterparts with the half-odd-integer spins .
通过在对偶正方形晶格上与相应的零场（对称）八顶点模型建立严格的映射等价关系，精确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联合杰克（中心正方形）晶格上的混合自旋 - 1/2和自旋 - 1伊辛模型。利用零场八顶点模型的图论或自旋表示这两种独立方法，对上述精确映射等价性进行了严格证明。特别研究了相互作用各向异性以及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一个与其他三个不同的三重态相互作用的各向异性模型时，所考虑的模型表现出具有恒定临界指数的强普适临界行为。相反，具有两个彼此成对相等的不同三重态相互作用的各向异性模型表现出弱普适临界行为，其临界指数随三重态相互作用以及单轴单离子各向异性的相对强度连续变化。证明了具有整数值自旋的混合自旋伊辛模型的临界指数变化与具有半奇数整数自旋的对应模型基本不同。
