Abstract
A projection operator which maps the q-state Potts model onto an Ising model is investigated. The case of an approximate mapping between two-spin nearest-neighbour clusters on a d-dimensional hypercubic lattice is considered. In the ferromagnetic case, first-order transitions occur for q>qc(d)=1+exp(2KIc(d))>or=2, where KIc(d) is the critical Ising coupling. Among the results are qc(d) to exp(2/(d-1)) as d to 1+, qc(2)=3.41 and qc(3)=2.56. The antiferromagnetic Potts model has no long range order for q>2.
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