Quantized noncommutative geometry from multitrace matrix models

In this paper, the geometry of quantum gravity is quantized in sense being noncommutative (first quantization) but it also emergent (second quantization). A new mechanism for proposed which can emerge from “one-matrix multitrace scalar matrix models” by probing statistical physics commutative phases matter. This contrast to usual emerges “many-matrix singletrace Yang–Mills gauge theory. novel scenario, form a transition between two phase diagrams real quartic model and phi-four field More precisely, emergence identified here with uniform-ordered corresponding (Ising) (stripe) coexistence lines. The critical exponents Wigner’s semicircle law are used determine dimension metric, respectively. Arguments saddle point equation, Monte Carlo simulation renormalization group equation provided support scenario.