2006/02/07 by Shu-Chiuan Chang, Robert Shrock
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algorithm #Chiral Potts curve #Combinatorics #Conjecture #Geometry #Ising model #Lattice (music) #Locus (genetics) #Mathematical analysis #Mathematical physics #Mathematics #Partition (number theory) #Partition function (quantum field theory) #Physics #Potts model #Quantum mechanics #Random Matrices and Applications #STRIPS #Square (algebra) #Square lattice #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1142/s021797920703703x
published as Int. J. Mod. Phys. B21, 1755-1773 (2007) · 10 pages, 6 figures
arxiv created 2006/02/07 · openalex publication_date 2007/04/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We calculate the partition function Z(G, Q, v) of the Q-state Potts model exactly for self-dual cyclic square-lattice strips of various widths L y and arbitrarily large lengths L x , with Q and v restricted to satisfy the relation Q=v 2 . From these calculations, in the limit L x →∞, we determine the continuous accumulation locus [Formula: see text] of the partition function zeros in the v and Q planes. A number of interesting features of this locus are discussed and a conjecture is given for properties applicable to arbitrarily large width. Relations with the loci [Formula: see text] for general Q and v are analyzed.