TY - JOUR

T1 - General structural results for Potts model partition functions on lattice strips

AU - Chang, Shu Chiuan

AU - Shrock, Robert

N1 - Funding Information:
The research of R. S. was supported in part by the NSF grant PHY-0098527.

PY - 2002/12/15

Y1 - 2002/12/15

N2 - We present a set of general results on structural features of the q-state Potts model partition function Z(G,q,v) for arbitrary q and temperature Boltzmann variable v for various lattice strips of arbitrarily great width Ly vertices and length Lx vertices, including (i) cyclic and Möbius strips of the square and triangular lattices, and (ii) self-dual cyclic strips of the square lattice. We also present an exact solution for the chromatic polynomial for the cyclic and Möbius strips of the square lattice with width Ly=5 (the greatest width for which an exact solution has been obtained so far for these families). In the Lx→∞ limit, we calculate the ground-state degeneracy per site, W(q) and determine the boundary ℬ across which W(q) is singular in the complex q plane.

AB - We present a set of general results on structural features of the q-state Potts model partition function Z(G,q,v) for arbitrary q and temperature Boltzmann variable v for various lattice strips of arbitrarily great width Ly vertices and length Lx vertices, including (i) cyclic and Möbius strips of the square and triangular lattices, and (ii) self-dual cyclic strips of the square lattice. We also present an exact solution for the chromatic polynomial for the cyclic and Möbius strips of the square lattice with width Ly=5 (the greatest width for which an exact solution has been obtained so far for these families). In the Lx→∞ limit, we calculate the ground-state degeneracy per site, W(q) and determine the boundary ℬ across which W(q) is singular in the complex q plane.

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U2 - 10.1016/S0378-4371(02)01028-2

DO - 10.1016/S0378-4371(02)01028-2

M3 - Article

AN - SCOPUS:0037114548

VL - 316

SP - 335

EP - 379

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-4

ER -