TY - JOUR

T1 - Exact Potts model partition function on strips of the triangular lattice

AU - Chang, Shu Chiuan

AU - Shrock, Robert

N1 - Funding Information:
The research of R.S. was supported in part at Stony Brook by the US NSF grant PHY-97-22101 and at Brookhaven by the US DOE contract DE-AC02-98CH10886. 4 4

PY - 2000/10/15

Y1 - 2000/10/15

N2 - In this paper we present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex strip graphs, of width Ly = 2 and arbitrary length, of the triangular lattice with free, cyclic, and Mobius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T = 0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Comparisons are made with our previous exact calculation of Potts model partition functions for the corresponding strips of the square lattice. Our present calculations yield, as special cases, several quantities of graph-theoretic interest.

AB - In this paper we present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex strip graphs, of width Ly = 2 and arbitrary length, of the triangular lattice with free, cyclic, and Mobius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T = 0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Comparisons are made with our previous exact calculation of Potts model partition functions for the corresponding strips of the square lattice. Our present calculations yield, as special cases, several quantities of graph-theoretic interest.

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U2 - 10.1016/S0378-4371(00)00225-9

DO - 10.1016/S0378-4371(00)00225-9

M3 - Article

AN - SCOPUS:0034301186

SN - 0378-4371

VL - 286

SP - 189

EP - 238

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

ER -