# 2D Quantum Gravity -Three States of Surfaces-

## TL;DR

This paper investigates the phase structure of two-dimensional random surfaces using dynamical triangulation, identifying three distinct phases and proposing a new method to detect branched polymers through baby universe analysis.

## Contribution

It introduces a new probe based on baby universe analysis to distinguish branched polymer phases in 2D quantum gravity models.

## Key findings

- Identification of three phases: flat, crumpled, and branched polymer.
- Development of a new method to detect branched polymers via baby universe analysis.
- Observation of drastic size distribution changes at phase transition points.

## Abstract

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.