Quenching 2D Quantum Gravity

TL;DR

This paper explores the critical behavior of the Ising model on fixed random $b3$ graphs, providing insights into quenched 2D quantum gravity by comparing with other graph ensembles and flat lattices.

Contribution

It introduces a simulation of the Ising model on quenched random graphs, highlighting differences from annealed models and previous studies on dynamical graphs.

Findings

Critical exponents differ from those on dynamical graphs

Quenched coupling shows distinct phase transition behavior

Results enhance understanding of 2D quantum gravity models

Abstract

We simulate the Ising model on a set of fixed random $\phi^3$ graphs, which corresponds to a {\it quenched} coupling to 2D gravity rather than the annealed coupling that is usually considered. We investigate the critical exponents in such a quenched ensemble and compare them with measurements on dynamical $\phi^3$ graphs, flat lattices and a single fixed $\phi^3$ graph.