  We reconsider the criticality of the Ising model on two-dimensional dynamical
triangulations based on the N-by-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.
