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 (23)

• The antiferromagnetic transition for the square-lattice Potts model
• On three-point connectivity in two-dimensional percolation
• Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator
• Universal ratios along a line of critical points. The Ashkin--Teller model
• A constrained Potts antiferromagnet model with an interface representation
• Potts q-color field theory and scaling random cluster model
• 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
• Finite-temperature phase transition in a class of 4-state Potts antiferromagnets
• Fields, particles and universality in two dimensions
• Exact results for quenched bond randomness at criticality
• The composite operator T\bar{T} in sinh-Gordon and a series of massive minimal models
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
• Factorization of correlations in two-dimensional percolation on the plane and torus
• Universal amplitude ratios of two-dimensional percolation from field theory
• On superuniversality in the $q$-state Potts model with quenched disorder
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• On the space of quantum fields in massive two-dimensional theories
• The antiferromagnetic Potts model
• Phase Diagram of the Square-Lattice Three-State Potts Antiferromagnet with Staggered Polarization Field
• Crossing probability and number of crossing clusters in off-critical percolation
• Sine-Gordon description of the scaling three-state Potts antiferromagnet on the square lattice

Cited by in corpus (19)

• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Majorana Loop Models for Measurement-Only Quantum Circuits
• On superuniversality in the $q$-state Potts model with quenched disorder
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
• Critical lines in the pure and disordered $O(N)$ model
• The three-state Potts antiferromagnet on plane quadrangulations
• Particles, conformal invariance and criticality in pure and disordered systems
• Ferromagnetic Potts models with multisite interaction
• On the phase diagram of the random bond $q$-state Potts model
• Critical points in the $R{P}^{N-1}$ model
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Critical points in coupled Potts models and correlated percolation
• Critical points in the $C{P}^{N-1}$ model
• Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes
• Nonuniversality in random criticality
• Maximally Random Discrete-Spin Systems with Symmetric and Asymmetric Interactions and Maximally Degenerate Ordering
• Exact results for spin glass criticality