Classifying Potts critical lines

2017/07/31 by Gesualdo Delfino, Elena Tartaglia
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Antiferromagnetism #Chiral Potts curve #Combinatorics #Condensed matter physics #Critical point (mathematics) #Ferromagnetism #Fixed point #Invariant (physics) #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Potts model #Quantum mechanics #Renormalization group #Scale invariance #Scattering #Square lattice #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1103/physreve.96.042137

published as Phys. Rev. E 96, 042137 (2017) · 15 pages, 2 figures, 2 tables; published version

arxiv created 2017/10/16 · openalex publication_date 2017/10/16 · arxiv updated 2017/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 we 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.

Citations

• On the space of quantum fields in massive two-dimensional theories
• Universal ratios along a line of critical points. The Ashkin–Teller model
• Infinite conformal symmetry in two-dimensional quantum field theory
• The antiferromagnetic Potts model
• q colourings of the triangular lattice
• The antiferromagnetic transition for the square-lattice Potts model
• Conformal Field Theory