Constraints on Beta Functions from Duality

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.

LaTeX, 6 pages

References in corpus (2)

• Duality Symmetries from Non--Abelian Isometries in String Theories
• Duality Transformations Away From Conformal Points

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