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Critical couplings and string tensions from two-lattice matching of RG decimations

Critical couplings and string tensions in SU(2) and SU(3) lattice gauge theory are calculated by two-lattice matching of RG block transformations. The transformations are of the potential moving type generating plaquette actions with large number of group characters and exhibit rapid approach to a unique renormalized trajectory. Fixing the critical coupling $β(N_τ)$ at one value of temporal lattice extent $N_τ$ by MC simulation, the critical couplings for other values of $N_τ$ are then obtained by lattice matching of these decimations. $β(N_τ)$ values are thus obtained for a range of $N_τ$ and found to be in agreement with MC simulation results to within a few percent in all cases. A similar procedure allows the calculation of string tensions for a range of $β$ values with similarly good agreement with MC data.