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Constraints on Beta Functions from Duality

P. H. Damgaard·P. E. Haagensen
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Abstract

We analyze the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. A consistency condition we propose shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the 2-d Ising model, and used towards finding the exact beta function of the $q$-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.

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P. H. Damgaard, P. E. Haagensen. 1996-09-30. Constraints on Beta Functions from Duality. https://doi.org/10.1088/0305-4470%2F30%2F13%2F019

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