Exact Potts model partition functions on strips of the honeycomb lattice

We present exact calculations of the partition function of the q-state Potts model on (i) open, (ii) cyclic, and (iii) Möbius strips of the honeycomb (brick) lattice of width L_y=2 and arbitrarily great length. In the infinite-length limit the thermodynamic properties are discussed. The continuous locus of singularities of the free energy is determined in the q plane for fixed temperature and in the complex temperature plane for fixed q values. We also give exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the Potts antiferromagnet for honeycomb strips of type (iv) L_y=3, cyclic, (v) L_y=3, Möbius, (vi) L_y=4, cylindrical, and (vii) L_y=4, open. In the infinite-length limit we calculate W(q) and determine the continuous locus of points where it is nonanalytic. We show that our exact calculation of the entropy for the L_y=4 strip with cylindrical boundary conditions provides an extremely accurate approximation, to a few parts in 10⁵ for moderate q values, to the entropy for the full 2D honeycomb lattice (where the latter is determined by Monte Carlo measurements since no exact analytic form is known).