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.
UR - http://www.scopus.com/inward/record.url?scp=0035877523&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035877523&partnerID=8YFLogxK
U2 - 10.1006/aphy.2001.6143
DO - 10.1006/aphy.2001.6143
M3 - Article
AN - SCOPUS:0035877523
SN - 0003-4916
VL - 290
SP - 124
EP - 155
JO - Annals of Physics
JF - Annals of Physics
IS - 2
ER -