Knot theory and statistical mechanics
Knot theory and statistical mechanics
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DOI：
10.1103/revmodphys.64.1099
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发表时间：
1992-10
影响因子：
44.1
通讯作者：
F. Y. Wu
中科院分区：
文献类型：
--
作者：
F. Y. Wu
最近的发展，在数学理论的纽结使用统计力学的方法进行检查。我们表明，结不变量可以通过考虑晶格上的统计力学模型来获得。特别地，我们建立了考夫曼括号多项式是Perk和Wu先前考虑的q态顶点模型的配分函数，而琼斯多项式是由q 2态Potts模型配分函数生成的。进一步的新纽结和链环不变量的生成非常依赖于对某些杨巴克斯特方程解的计算机辅助研究。
Recent development in the mathematical theory of knots using the method of statistical mechanics is examined. We show that knot invariants can be obtained by considering statistical‐mechanical models on a lattice. Particularly, we establish that the Kauffman’s bracket polynomial is the partition function of a q‐state vertex model previously considered by Perk and Wu, and that the Jones polynomial is generated by a q 2‐state Potts model partition function. The generation of further new knot and link invariants many very well rely on computed‐aided studies of solutions of certain Yang‐Baxter equations.