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Critical couplings and string tensions via lattice matching of RG 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 RG 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 $β_c(N_τ)$ at one value of temporal lattice length $N_τ$ by MC simulation, the critical couplings for any other value of $N_τ$ are then obtained by lattice matching of the block decimations. We obtain $β_c(N_τ)$ values over the range $N_τ= 3 - 32$ 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.