The Branching of Graphs in 2-d Quantum Gravity

TL;DR

This paper calculates the branching ratio for various 2d gravity models using dynamical planar graphs, providing insights into the structure and phase transitions of these models.

Contribution

It introduces a method to compute the branching ratio for different 2d gravity models, aiding in identifying phase transitions and structural properties.

Findings

Branching ratios vary across models.

Estimates the phase transition point for the Ising model.

Provides a quantitative measure of graph structure in 2d gravity.

Abstract

The branching ratio is calculated for three different models of 2d gravity, using dynamical planar phi-cubed graphs. These models are pure gravity, the D=-2 Gaussian model coupled to gravity and the single spin Ising model coupled to gravity. The ratio gives a measure of how branched the graphs dominating the partition function are. Hence it can be used to estimate the location of the branched polymer phase for the multiple Ising model coupled to 2d gravity.