Investigating the critical properties of beyond-QCD theories using Monte Carlo Renormalization Group matching

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Monte Carlo Renormalization Group (MCRG) methods were designed to study the non-perturbative 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 non-perturbative 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.