Jose Maria P. Balmaceda
Department of Mathematics, College of Science
University of the Philippines
doi.org/10.57043/transnastphl.1997.5919
Abstract
The construction of new and powerful invariants of knots and links by Vaughan Jones in 1984 and its recent generalizations have led to the discovery of important connections between the theory of knots and other branches of mathematics and sciences. The new knot theory has already been useful to molecular biologists studying the double helices of DNA. In physics. models in statistical mechanics may be defined on a knot or link diagram so that a suitable variation of the partition function of the system is often a knot invariant. In 1989, Jones constructed spin models and posed the challenge of investigating combinatorial structures for sources of spin models. In this paper we present an approach, first observed by Francois Jaeger in 1992, to the study of spin models using a combinatorial object called an association scheme. We outline the background and method of this approach and prove several characterization theorems for spin models arising from some families of association schemes.”