Critical couplings and string tensions via lattice matching of renormalization group decimations

We calculate critical couplings and string tensions in SU(2) and SU(3) pure lattice gauge theory by a simple and inexpensive technique of two-lattice matching of renormalization group block transformations. The transformations are potential moving decimations generating plaquette actions with large number of group characters and exhibit rapid approach to a unique renormalized trajectory. Fixing the critical coupling beta(c)(N-tau) at one value of temporal lattice length N-tau by Monte Carlo (MC) simulation, the critical couplings for any other value of N-tau are then obtained by lattice matching of the block decimations. We obtain beta(c)(N-tau) values over the range N-tau = 3-32 and find agreement with MC simulation results to within a few percent in all cases. A similar procedure allows the calculation of string tensions with similarly good agreement with MC data.