Pure and dilute Z(N) spin and generalised gauge lattice systems: duality and criticality

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Abstract
Considers the pure Z(N) spin systems (including the standard Ising and Potts models) as well as generalised gauge systems (plaquettes or more complex simplex) in d-dimensional hypercubic lattices. These models are self-dual, and the authors show how this duality can be thought of as a series-parallel transformation. The simplicity of the equations enables conjectures to be made on the approximate critical frontier of the diluted version of the above systems, including some particular asymptotic behaviours which are exact. As an illustration the d=2 diluted Z(4) spin system is discussed in some detail: for those regions where exact results are available the agreement is satisfactory.

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