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

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.