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 $q>\mathrm{}{q}_c\mathrm{}\left(d\right)\mathrm{}$ 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 $\mathrm{hT}$ plane. Using Padé approximants we obtain for $d=2\mathrm{}$ 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 to find the exact location and nature of the critical point in this limit.

• Received 30 December 1980

DOI:https://doi.org/10.1103/PhysRevB.24.1374