Phase diagram of the Potts model in an applied field

We use the technique of large-q expansion to investigate the phase diagram of the q-state Potts model in an applied field favoring order in one state. The method is valid for any number of dimensions. We find that for q>q/sub C/ (d) there is a first-order phase boundary starting at the zero-field transition point and terminating in a critical point in the interior of the hT plane. Using Pade approximants we obtain for d = 2 the shape and location of this line for various values of q. We also develop a lattice-gas expansion for any d which enables us, in the limit of large but finite q, to map the problem into an equivalent Ising expansion and thus find the exact location and nature of the critical point in this limit