The Ising transition in 2D simplicial quantum gravity - can Regge calculus be right?

TL;DR

This study uses high-statistics simulations to investigate the Ising transition in 2D quantum gravity via Regge calculus, finding that critical exponents match static lattice values rather than dynamic predictions, challenging prior expectations.

Contribution

It provides the first definitive evidence that Ising critical exponents in 2D quantum gravity align with static lattice values, not those predicted by dynamical triangulation models.

Findings

Critical exponents match Onsager values for static lattices.

Excludes predicted critical exponents for dynamical triangulation.

Results are consistent across different coupling strengths of R^2 term.

Abstract

We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to $512^2$ vertices. For the constant area ensemble and the $dl/l$ functional measure we definitively can exclude the critical exponents of the Ising phase transition as predicted for dynamically triangulated surfaces. We rather find clear evidence that the critical exponents agree with the Onsager values for static regular lattices, independent of the coupling strength of an $R^2$ interaction term. For exploratory simulations using the lattice version of the Misner measure the situation is less clear.