Constraints on Beta Functions from Duality

Details Constraints on Beta Functions from Duality Constraints on Beta Functions from Duality

1996-09-25

arxiv.org/abs/cond-mat/9609242v2

J.Phys.A30:4681-4686,1997

Physics

Condensed Matter

LaTeX, 6 pages

Scientific paper

10.1088/0305-4470/30/13/019

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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