Phase diagrams of the random-field Potts model in three dimensions

We develop and perform $\frac{1}{q}$ expansions for the $q$-state Potts model in a random field. The expansion parameter is $z=\frac{1}{q^{\frac{1}{3}}}$ in three dimensions, and we calculate to $O\left(z^{12}\right)$ using the Padé method for resummation. A phase diagram is constructed and a transition into an ordered state is found. For $q>~3$ the transition is of first order, and for $q=2\mathrm{}$ (Ising model) we find the location of the tricritical point.