Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and [Formula Presented] the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width [Formula Presented] and [Formula Presented] vertices and arbitrarily great length [Formula Presented] vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the [Formula Presented] (Ising) and [Formula Presented] Potts antiferromagnets have zero-temperature critical points on the [Formula Presented] limits of the strips that we study. With the generalization of q from [Formula Presented] to C, we determine the analytic structure of [Formula Presented] in the q plane for the various cases.