Effective-Spin Model for Finite-Temperature QCD

An effective-spin model for finite-temperature QCD is derived by use of a variant of the Migdal-Kadanoff renormalization group. Mean field theory and [for SU(3)] Monte Carlo simulation are applied to the model in order to find the deconfining phase transition. The results are in very good agreement with Monte Carlo simulations of the full theory. Mean field theory predicts that the deconfining transition in pure $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ lattice gauge theory is first order for all $N>~3$.