Potts models, which can be used to analyze dependent observations on a spatial field, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. However, because of the involvement of an in-tractable normalizing constant, inference for Potts model is computationally expensive for large spatial fields. We propose ordered conditional approximations that enable fast evaluation of Potts likelihoods and rapid inference on hidden Potts fields. The computational complexity of our approximation methods is linear in the number of spatial locations. We illustrate the advantages of our approach using simulated data and real observations.