  Large $N$ matrix models modified by terms of the form $ g(\Tr\Phi^n)^2$
generate random surfaces which touch at isolated points. Matrix model results
indicate that, as $g$ is increased to a special value $g_t$, the string
susceptibility exponent suddenly jumps from its conventional value $\gamma$ to
${\gamma\over\gamma-1}$. We study this effect in \L\ gravity and attribute it
to a change of the interaction term from $O e^{\alpha_+ \phi}$ for $g<g_t$ to
$O e^{\alpha_- \phi}$ for $g=g_t$ ($\alpha_+$ and $\alpha_-$ are the two roots
of the conformal invariance condition for the \L\ dressing of a matter operator
$O$). Thus, the new critical behavior is explained by the unconventional branch
of \L\ dressing in the action.
