Finite temperature phase transition of a scalar field on a fuzzy sphere

We study finite temperature phase transition of neutral scalar field on a fuzzy sphere using Monte Carlo simulations. We work with the zero mode in the temporal directions, while the effects of the higher modes are taken care by the temperature dependence of r. In the numerical calculations we use "pseudo- heatbath" method which reduces the autocorrelation considerably. Our results agree with the conventional calculations. We report some new results which show the presence of meta-stable states, first order symmetry breaking transition and existence of multiple triple points in the phase diagram.