This entry contributed by S. T. Wierzchon
The statistical mechanics model obtained by assuming that each individual can be in one of q (where q > 2) states in the Ising model. The computation of the partition function is a very hard problem. However, V. F. R. Jones observed an amazing connection between this problem and knot theory. Eric Weisstein's World of Math He showed that for the Potts model, the partition function generates the Jones polynomial Eric Weisstein's World of Math V(t), where t and q (the number of states) are related by the equation
References
Adams, C. C. The Knot Book. New York: W. H. Freeman, §7.4 and 8.3, 1994.
Jones, V. F. R. "On Knot Invariants Related to Some Statistical Mechanical Models." Pacific J. Math. 137, 311-334, 1989.
Kauffman, L. Knots and Physics, 2nd ed. World Scientific, 364-380, 1993.
Wu, F. Y. "Jones Polynomial as a Potts Model Partition Function." J. Knot Th. Ramifications 1, 47-57, 1992.
