The Ising model on 2d dynamical triangulations was originally introduced by Kazakov in 1986, which is a statistical system including gravitational degrees of freedom. This system is known to be critical at the finite temperature and the continuum theory defined around the critical point is the 2d gravity minimally coupled to fermions.

We introduce a (non-thermal) external parameter to the system, aiming at observing the quantum critical behavior. Tuning the parameter to a certain value the critical temperature reaches absolute zero and the resulting continuum theory at the zero temperature is NOT the 2d gravity minimally coupled to fermions. As it turns out, physics at the zero-temperature differs depending on the "cool down speed".

The talk will be based on the work with Tomo Tanaka (Phys.Rev. D98 (2018) no.2, 026026) and the work in progress with Jan Ambjorn.