Studies of Model Systems in Statistical Mechanics and Quantum Field Theory

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9404747 This renewal grant involves research on solvable models for statistical mechanics and quantum field theory. Work will be done on extending research on the excitations and the completeness rules to the full phase diagram of the three-state chiral Potts model. It will be determined how the excitation spectrum of the ferromagnetic and massively superintegrable cases, which have strikingly different features, actually join together in a smooth fashion. The manner in which the level crossing phenomena of the massless incommensurate phase allows for the systems to continuously go from the ferromagnetic case to the antiferromagnetic case will be studied. Investigations of the fermionic sum representations of characters will be extended by finding the representations for the twisted affine and super algebras. %%% This theoretical research is at the interface between condensed matter physics, mathematical physics and applied mathematics. Using powerful mathematical techniques, connections between quantum field theory and statistical mechanics will be utilized to understand the properties of various condensed matter systems at a fundamental level.