2D quantum gravity: Three states of surfaces

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 structures of surfaces in the two-dimensional parameter space are classified into three states: flat surface, 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 by using the analysis of minimum neck baby universe. This method can clearly distinguish the branched polymer phase from others according to the sizes and arrangements of baby universes. The size and arrangement of baby universes change drastically for each state. The phases of surfaces coupled with multi-Ising spins are studied in a similar manner.