  The random field q-States Potts model is investigated using exact
groundstates and finite-temperature transfer matrix calculations. It is found
that the domain structure and the Zeeman energy of the domains resembles for
general q the random field Ising case (q=2), which is also the expectation
based on a random-walk picture of the groundstate. The domain size distribution
is exponential, and the scaling of the average domain size with the disorder
strength is similar for q arbitrary. The zero-temperature properties are
compared to the equilibrium spin states at small temperatures, to investigate
the effect of local random field fluctuations that imply locally degenerate
regions. The response to field pertubabtions ('chaos') and the susceptibility
are investigated. In particular for the chaos exponent it is found to be 1 for
q = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is
studied for correlated random fields.
