The Six-Vertex Model
The Six-Vertex Model
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六顶点模型
DOI：
10.1007/978-3-662-03843-7_10
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
G. M. Bell
中科院分区：
文献类型：
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作者：
D. Lavis;G. M. Bell
在这一章中，我们考虑一类二维模型的精确解，它们与伊辛模型具有完全不同的行为。这些模型是基于完全氢键网络的正方形晶格版本，就像冰I一样（见附录A.3）。当所有的键构型具有相等的能量时，自由能与d = 2的冰类似物（方形冰）的基态（零点）熵有关，这是由Lieb（1967 a）估算的。和水一样，某些其他物质，如KH2PO4（磷酸二氢钾），结晶为四配位的氢键网络。KH_2PO_4是一种铁电体，在低于临界温度的零场下，它具有自发极化。铁电体和反铁电体的正方形晶格类似物可以通过对各种键构型进行适当的能量分配来构造。Lieb（1967 b，1967 c）通过扩展用于方形冰的方法得到了这些模型的自由能表达式。与伊辛模型相反，对于非零场（在这种情况下是电场），可以得到一些结果（Sutherland 1967，Lieb 1969）。本章的发展是基于Lieb和Wu（1972）的广泛评论文章。
In this chapter we consider exact solutions for a class of two-dimensional models which have completely different behaviour from the Ising model. These models are based on a square lattice version of a completely hydrogen-bonded network, like that of ice I (see Appendix A.3). With all bond configurations having equal energy, the free energy is related to the ground-state (zero-point) entropy of a d = 2 ice analogue (square ice), which was evaluated by Lieb (1967a). As well as water, certain other substances, such as KH2PO4 (potassium dihydrogen phosphate), crystallize as four-coordinated hydrogen-bonded networks. KH2PO4 is a ferroelectric with a spontaneous electrical polarization in zero field below a critical temperature. Square lattice analogues of ferroelectrics and antiferroelectrics can be constructed by appropriate assignment of energies to the various bond configurations. Lieb (1967b, 1967c) obtained expressions for the free energy of these models by an extension of the method used for square ice. In contrast to the Ising model, some results can be obtained for non-zero fields (electric fields in this case) (Sutherland 1967, Lieb 1969). The development in this chapter is based on the extensive review article of Lieb and Wu (1972).