Universality of coupled Potts models

Details Universality of coupled Potts models Universality of coupled Potts models

2001-12-07

arxiv.org/abs/cond-mat/0112120v1

Physics

Condensed Matter

Statistical Mechanics

29 pages, 3 figures

Scientific paper

10.1016/S0550-3213(02)00213-4

We study systems of M Potts models coupled by their local energy density. Each model is taken to have a distinct number of states, and the permutational symmetry S_M present in the case of identical coupled models is thus broken initially. The duality transformations within the space of 2^M-1 multi-energy couplings are shown to have a particularly simple form. The selfdual manifold has dimension D_M = 2^{M-1}-1. Specialising to the case M=3, we identify a unique non-trivial critical point in the three-dimensional selfdual space. We compare its critical exponents as computed from the perturbative renormalisation group with numerical transfer matrix results. Our main objective is to provide evidence that at the critical point of three different coupled models the symmetry S_3 is restored.

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