  Enormous advances have been made in the past 20 years in our understanding of
the random-field Ising model, and there is now consensus on many aspects of its
behavior at least in thermal equilibrium. In contrast, little is known about
its generalization to the random-field Potts model which has wide-ranging
applications. Here we start filling this gap with an investigation of the
three-state random-field Potts model in three dimensions. Building on the
success of ground-state calculations for the Ising system, we use a recently
developed approximate scheme based on graph-cut methods to study the properties
of the zero-temperature random fixed point of the system that determines the
zero and non-zero temperature transition behavior. We find compelling evidence
for a continuous phase transition. Implementing an extensive finite-size
scaling (FSS) analysis, we determine the critical exponents and compare them to
those of the random-field Ising model.
