TY - JOUR

T1 - Ground state entropy of the potts antiferromagnet on triangular lattice strips

AU - Chang, Shu Chiuan

AU - Shrock, Robert

N1 - Funding Information:
The research of R.S. was supported in part by the U.S. NSF Grant PHY-97-22101.

PY - 2001/6/15

Y1 - 2001/6/15

N2 - 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 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 for Ly=3, 4, (b) (FBCy, TPBCx) = Möbius, Ly=3, (c) (PBCy, PBCx) = toroidal, Ly=3, (d) (PBCy, TPBCx) = Klein bottle, Ly=3, (e) (PBCy, FBCx) = cylindrical, Ly=5, 6, and (f) (FBCy, FBCx) = free, Ly=5, where F, P, and TP denote free, periodic, and twisted periodic. 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 B where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci 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. Some results are given for strips of other lattices.

AB - 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 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 for Ly=3, 4, (b) (FBCy, TPBCx) = Möbius, Ly=3, (c) (PBCy, PBCx) = toroidal, Ly=3, (d) (PBCy, TPBCx) = Klein bottle, Ly=3, (e) (PBCy, FBCx) = cylindrical, Ly=5, 6, and (f) (FBCy, FBCx) = free, Ly=5, where F, P, and TP denote free, periodic, and twisted periodic. 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 B where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci 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. Some results are given for strips of other lattices.

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U2 - 10.1006/aphy.2001.6143

DO - 10.1006/aphy.2001.6143

M3 - Article

AN - SCOPUS:0035877523

VL - 290

SP - 124

EP - 155

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -