2005/11/30 by Jesper Lykke Jacobsen, Jean-Francois Richard, Jean‐François Richard +2 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.nuclphysb.2006.02.033
published as Nuclear Physics B 743 (2006) 153-206 · 60 pages, 16 figures, 2 tables
arxiv created 2006/02/17 · openalex publication_date 2006/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the phase diagram of Q-state Potts models, for Q=4 cos2(PI/p) a Beraha number (p>2 integer), in the complex-temperature plane. The models are defined on L x N strips of the square or triangular lattice, with boundary conditions on the Potts spins that are periodic in the longitudinal (N) direction and free or fixed in the transverse (L) direction. The relevant partition functions can then be computed as sums over partition functions of an A_p-1 type RSOS model, thus making contact with the theory of quantum groups. We compute the accumulation sets, as N -> infinity, of partition function zeros for p=4,5,6,infinity and L=2,3,4 and study selected features for p>6 and/or L>4. This information enables us to formulate several conjectures about the thermodynamic limit, L -> infinity, of these accumulation sets. The resulting phase diagrams are quite different from those of the generic case (irrational p). For free transverse boundary conditions, the partition function zeros are found to be dense in large parts of the complex plane, even for the Ising model (p=4). We show how this feature is modified by taking fixed transverse boundary conditions.