Criticality at absolute zero from Ising model on two-dimensional dynamical triangulations

TL;DR

This paper explores the critical behavior of the Ising model on 2D dynamical triangulations, revealing that the critical temperature can reach absolute zero through tuning parameters, leading to a novel continuum theory.

Contribution

It introduces a loop-counting parameter and linear potential terms in the matrix model, showing how to tune the critical temperature to zero in the large-N limit.

Findings

Critical temperature can be tuned to absolute zero.

The continuum theory differs from pure gravity or gravity with conformal matter.

The model exhibits a new quantum gravity phase with central charge 1/2.

Abstract

We reconsider the criticality of the Ising model on two-dimensional dynamical triangulations based on the $N \times N$ hermitian two-matrix model with the introduction of a loop-counting parameter and linear terms in the potential. We show that in the large-N limit even though the Ising model is classical, the critical temperature can reach absolute zero by tuning the loop-counting parameter, and the corresponding continuum theory turns out to be the quantised theory of neither pure gravity nor gravity coupled to conformal matter with central charge being 1/2.