2000/04/13 by Shu-Chiuan Chang, Robert Shrock · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Antiferromagnetism #Boundary value problem #Exponent #Ground state #Hexagonal lattice #Lattice (music) #Physics of Superconductivity and Magnetism #Potts model #Quasicrystal Structures and Properties #STRIPS #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat #math-ph #math.MP
paper · pdf · doi:10.1006/aphy.2001.6143
published as Annals Phys. 290 (2001) 124-155 · 50 pages, latex, 6 encapsulated postscript figures
arxiv created 2000/04/13 · openalex publication_date 2001/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present exact calculations of the zero-temperature partition function (chromatic polynomial) P for the q-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length Lx vertices and of width Ly=3 vertices and, in the Lx → ∞ limit, the exponent of the ground-state entropy, W=eS0/kB. The strips considered, with their boundary conditions (BC) are (a) (FBCy,PBCx)= cyclic, (b) (FBCy,TPBCx)= Möbius, (c) (PBCy,PBCx)= toroidal, and (d) (PBCy,TPBCx)= Klein bottle, where F, P, and TP denote free, periodic, and twisted periodic. Exact calculations of P and W are also given for wider strips, including (e) cyclic, Ly=4, and (f) (PBCy,FBCx)= cylindrical, Ly=5,6. Several interesting features are found, including the presence of terms in P proportional to cos(2πLx/3) for case (c). The continuous locus of points \cal B where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci \cal B for families with different boundary conditions. Numerical values of W are given for infinite-length strips of various widths and are shown to approach values for the 2D lattice rapidly. A remark is also made concerning a zero-free region for chromatic zeros.