  Two-dimensional random surfaces are studied numerically by the dynamical
triangulation method. In order to generate various kinds of random surfaces,
two higher derivative terms are added to the action. The phases of surfaces in
the two-dimensional parameter space are classified into three states: flat,
crumpled surface, and branched polymer. In addition, there exists a special
point (pure gravity) corresponding to the universal fractal surface. A new
probe to detect branched polymers is proposed, which makes use of the
minbu(minimum neck baby universe) analysis. This method can clearly distinguish
the branched polymer phase from another according to the sizes and arrangements
of baby universes. The size distribution of baby universes changes drastically
at the transition point between the branched polymer and other kind of surface.
The phases of surfaces coupled with multi-Ising spins are studied in a similar
manner.
