Exact fuzzy sphere thermodynamics in matrix quantum mechanics

We study thermodynamical properties of a fuzzy sphere in matrix wuantum mechanics of the BFSS type including the Chern-Simons term. Various quantities are calculated to all orders in perturbation theory exploiting the one-loop saturation of the effective action in the large-N limit. The fuzzy sphere becomes unstable at sufficiently strong coupling, and the critical point is obtained explicitly as a function of the temperature. The whole phase diagram is investigated by Monte Carlo simulation. Above the critical point, we obtain perfect agreement with the all order results. In the region below the criticalk point, which is not accessible by perturbation theory, we observe the Hagedorn transition. In high temperature limit our model is equivalent to a totally reduced model, and the relationship to previously known results is clarified.