  We consider discrete spin models on arbitrary planar graphs and lattices with
frustrated interactions. We first analyze the Ising model with frustrated
plaquettes. We use an algebraic approach to derive the result that an Ising
model with some of its plaquettes frustrated has a dual which is an Ising model
with an external field $i\pi/2$ applied to the dual sites centered at
frustrated plaquettes. In the case that all plaquettes are frustrated, this
leads to the known result that the dual model has a uniform field $i\pi/2$
whose partition function can be evaluated in the thermodynamic limit for
regular lattices.
  The analysis is extended to a Potts spin glass with analogous results
obtained.
