  Systems with a bulk first-order transition can display diverging correlation
lengths close to a surface. This surface induced disordering yields a special
type of surface criticality. Using extensive numerical simulations we study
surface quantities in the two-dimensional Potts model with a large number of
states $q$ which undergoes a discontinuous bulk transition. The surface
critical exponents are thereby found to depend on the value of $q$, which is in
contrast to prior claims that these exponents should be universal and
independent of $q$. It follows that surface induced disordering at first-order
transitions is characterized by exponents that depend on the details of the
model.
