A series expansion for the free energy of the q-state Potts model on a square lattice is used to estimate the specific heat critical exponents. The analysis is based on a series transformation which was suggested by the known solution of the two-state Potts (Ising) model, and which makes optimum use of the duality theorem. The transformed series is quite smooth. Neville tables yield the estimates alpha (2)=0.0001+or-0.0003 for the two-state model, alpha (3)=0.296+or-0.002 for the three-state model, and alpha (4)=0.45+or-0.02 for the four-state model. The value for alpha (3) differs considerably from one reported by Straley and Fisher (1973), and substantially improves compliance with the Rushbrooke inequality.
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