Abstract
The two-dimensional version of a generalised Ising gauge theory in which the gauge part of the action involves a product of Ising link variables around every rectangular 2*1 face of the lattice is studied. The pure gauge theory is related to the Ising model and is self-dual. The gauge plus matter theory is also self-dual. For negative gauge coupling an Ising critical line in the ( beta g, beta m) plane separates a phase with staggered frustration from another which is homogeneously frustrated.
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