Classifying Potts critical lines

Abstract

We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points invariant under the permutational symmetry $S_q$ in two dimensions, and show how one of these scattering solutions describes the ferromagnetic and square lattice antiferromagnetic critical lines of the $q$-state Potts model. Other solutions we determine should correspond to new critical lines. In particular, we obtain that a $S_q$-invariant fixed point can be found up to the maximal value $q=(7+\sqrt{17})/2$. This is larger than the usually assumed maximal value 4 and leaves room for a second order antiferromagnetic transition at $q=5$.

15 pages, 2 figures, 2 tables; published version

References in corpus (8)

• Confinement in the q-state Potts field theory
• Phase separation in a wedge. Exact results
• Parafermionic excitations and critical exponents of random cluster and O(n) models
• Fields, particles and universality in two dimensions
• The composite operator T\bar{T} in sinh-Gordon and a series of massive minimal models
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• On superuniversality in the $q$-state Potts model with quenched disorder
• On the space of quantum fields in massive two-dimensional theories

Cited by in corpus (1)

• On superuniversality in the $q$-state Potts model with quenched disorder