  We study the zero-temperature criticality of the Ising model on
two-dimensional dynamical triangulations to contemplate its physics. As it
turns out, an inhomogeneous nature of the system yields an interesting phase
diagram and the physics at the zero temperature is quite sensitive about how we
cool down the system. We show the existence of a continuous parameter that
characterizes the way we approach the zero-temperature critical point and it
may enter in a critical exponent.
