We reconsider the criticality of the Ising model on two-dimensional dynamical triangulations based on the N × 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 quantized theory of neither pure gravity nor gravity coupled to conformal matter with central charge being 1 / 2 .
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