Exact Partition Functions for the q-State Potts Model with a Generalized Magnetic Field on Lattice Strip Graphs.

We calculate the partition function of the q-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values $$\{1,\ldots ,s\}$$ with $$s \le q$$ . For the case of antiferromagnet spin-spin coupling, these provide exactly solved models that exhibit an onset of frustration and competing interactions in the context of a novel type of tensor-product $$S_s \otimes S_{q-s}$$ global symmetry, where $$S_s$$ is the permutation group on s objects. [ABSTRACT FROM AUTHOR]