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 $$\{1,\ldots ,s\}$${1,…,s} with $$s \le q$$s≤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 $$S_s \otimes S_{q-s}$$Ss⊗Sq-s global symmetry, where $$S_s$$Ss is the permutation group on s objects.