Investigating the critical properties of beyond-QCD theories using Monte Carlo renormalization group matching

Monte Carlo renormalization group (MCRG) methods were designed to study the nonperturbative phase structure and critical behavior of statistical systems and quantum field theories. I adopt the 2-lattice matching method used extensively in the 1980's and show how it can be used to predict the existence of nonperturbative fixed points and their related critical exponents in many flavor SU(3) gauge theories. This work serves to test the method and I study relatively well understood systems: the Nf=0, 4 and 16 flavor models. The pure gauge and Nf=4 systems are confining and chirally broken and the MCRG method can predict their bare step scaling functions. Results for the Nf=16 model indicate the existence of an infrared fixed point with nearly marginal gauge coupling. I present preliminary results for the scaling dimension of the mass at this new fixed point.