GL(2, Bbb R) dualities in generalised Z(2) gauge theories and Ising models

We study a class of duality transformations in generalised Z(2) gaugetheories and Ising models on two- and three-dimensional compact lattices. Thetheories are interpreted algebraically in terms of the structure constants of abidimensional vector space H with algebra and coalgebra structures, and it isshown that for any change of basis in H there is a related symmetry betweensuch models. The classical Kramers and Wannier dualities are described asspecial cases of these transformations. We derive explicit expressions for therelation between partition functions on general finite triangulations for thesecases, extending results known for square and cubic lattices in thethermodynamical limit. A class of symmetry transformations in which the gaugecoupling changes continuously is also studied in two dimensions.Comment: 29 pages, 4 figure