Series studies of the Potts model. III: The 3-state model on the simple cubic lattice

The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $3$-state Potts model on the simple cubic lattice to order $z^{43}$ and the high-temperature expansion of the partition function to order $v^{21}$. We use the numerical data to show that the transition is first-order, and estimate the latent heat, the discontinuity in the magnetisation, and a number of other critical parameters.