The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity

TL;DR

This paper introduces a block spin renormalization group method for two-dimensional quantum gravity using dynamical triangulation, demonstrating its effectiveness through application to the Ising model coupled to quantum gravity.

Contribution

It proposes a novel block spin RG approach for dynamical triangulation in 2D quantum gravity, linking lattice connectivity to a block metric.

Findings

Reproduces the correct critical coupling for the Ising model

Finite size effects obscure the critical exponent

Demonstrates the potential of the RG approach in quantum gravity contexts

Abstract

A block spin renormalization group approach is proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. The idea is to update link flips on the block lattice in response to link flips on the original lattice. Just as the connectivity of the original lattice is meant to be a lattice representation of the metric, the block links are determined in such a way that the connectivity of the block lattice represents a block metric. As an illustration, this approach is applied to the Ising model coupled to two-dimensional quantum gravity. The correct critical coupling is reproduced, but the critical exponent is obscured by unusually large finite size effects.