论文标题
具有交叉和四旋相互作用的二维ISING模型的残留熵
Residual Entropy of a Two-dimensional Ising Model with Crossing and Four-spin Interactions
论文作者
论文摘要
我们研究了具有交叉和四旋链相互作用的二维ISING模型的残留熵，这都是在零磁场和假想磁场I（π/2）KT中的情况。该ISIN模型的自旋构型可以用定义的氢键标准方向映射到方冰的氢构型中。利用与精确求解的八个vertex模型的等效性，并采用低温限制，我们获得了残留的熵。在零场中进行了两个可溶性病例，并检查了一个虚场中的一个可溶性病例。如果自由屈服条件在零字段中保持，我们发现低温限制的基态包括不服从冰规则的配置。在零字段中的另一种情况下，四旋转相互作用为 - {\ infty}，在虚场中，四旋旋转相互作用为0，残留熵与1967年Lieb确定的方形冰的结果完全一致。在后者的解决方案中，我们已经显示出与平方冰的残留冰冰问题的替代方法。
We study the residual entropy of a two-dimensional Ising model with crossing and four-spin interactions, both for the case that in zero magnetic field and that in an imaginary magnetic field i(π/2)kT. The spin configurations of this Ising model can be mapped into the hydrogen configurations of square ice with the defined standard direction of the hydrogen bonds. Making use of the equivalence of this Ising system with the exactly solved eight-vertex model and taking the low temperature limit, we obtain the residual entropy. Two soluble cases in zero field and one soluble case in imaginary field are examined. In the case that the free-fermion condition holds in zero field, we find the ground states in low temperature limit include the configurations disobeying the ice rules. In another case in zero field that the four-spin interactions are -{\infty}, and the case in imaginary field that the four-spin interactions are 0, the residual entropy exactly agrees with the result of square ice determined by Lieb in 1967. In the solutions of the latter two cases, we have shown alternative approaches to the residual entropy problem of square ice.
