Scaling study of pure gauge lattice QCD by Monte Carlo renormalization group method

The scaling behavior of pure gauge SU(3) in the region β=5.85-7.60 is examined by a Monte Carlo renormalization group analysis. The coupling shifts induced by factor 2 blocking are measured on both ${32}^4$ and ${16}^4$ lattices with high statistics. A systematic deviation from naive 2-loop scaling is clearly seen. The mean field and effective coupling constant schemes explain part, but not all, of the deviation. It can be accounted for by a suitable change of coupling constant, including a correction term O(${\mathit{g}}^7$) in the 2-loop lattice β function. Based on this improvement, √σ /${\mathrm{\Lambda }}_{\mathrm{MS}\mathrm{¯}\mathit{f}}^{\mathit{n}}$=0 is estimated to be 2.2±0.1 from the analysis of the string tension σ.