Abstract
Link polynomial, topological invariant for knots and links, is constructed from an exactly solvable model in statistical mechanics. A general theory consists of two steps. First, representation of the braid group is made from the Boltzmann weights of the exactly solvable model. Second, Markov trace is defined on the braid group representation. Sufficient conditions for the existence of the Markov trace are explicitly given. The knot theory based on exactly solvable models also includes braid-monoid algebra, graphical approach and two-variable extension of link polynomials. In addition, application of the theory to graph-state models is presented.
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