Abstract
By the Kasteleyn and Fortuin formulation, a Potts spin system can be expressed as a percolation system of spin clusters. The topological entropy can be defined from the number of spin cluster patterns as a function of the numbers of bonds and clusters. Using a self duality, the topological entropy is shown to have the maximum value at the transition temperature for the square lattice. It also shows a delicate singular structure around the transition point even at the unity degree of internal freedom, the one-state Potts model, as a unified generating function. The strongly-frustrated Ising system is understood as the one-state Potts model with the real spin clusters.
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