Non-perturbative Renormalization Group in Lattice Gauge Theory

Our main focus is on developing non-perturbative lattice renormalization schemes. Key concepts of contemporary theoretical physics such as universality, self-similarity, scaling, data collapse and asymptotic freedom are directly associated with the development of the renormalization group (RG) ideas. Non-perturbative renormalization group (RG) ideas arewidely used in the strong-correlated systems such as QCD and condense matter. We aim at developing some RG methods much cheaper than lattice Monte Carlo simulations, and they can be used as analytical analysis tool or a good guideline for full Monte Carlo simulations.We borrow some ideas from MK decimation and fermion block-spin RG methods, and develop a few new lattice RG schemes. The methods have been used to locate the conformal window and calculate some nite temperature physical quantities such as critical couplings and stringtensions. In general, the numeric results from our RG scheme are very close to full 4d Monte Carlo simulations which means we have caught some key aspects of lattice system. Our RG schemes take no-time in comparison to Monte Carlo simulation. By the schemes, we caneither solve some problems directly (eg. calculate beta function, locate conformal window) or convert the problem in a large lattice to the one in a small lattice (eg.critical coupling), and in both cases the computing time will be signicantly reduced