  We investigate the crumpling transition for a dynamically triangulated random
surface embedded in two dimensions using an effective model in which the
disordering effect of the $X$ variables on the correlations of the normals is
replaced by a long-range ``antiferromagnetic'' term. We compare the results
from a Monte Carlo simulation with those obtained for the standard action which
retains the $X$'s and discuss the nature of the phase transition.
