Convergence of Migdal-Kadanoff iterations in non-abelian lattice gauge models

We study the Migdal-Kadanoff recursion relations for lattice gauge models with gauge groups SU(N) or U(N) in dimensionsd<4. It is shown that the Gibbs factor of a plaquette with Wilson action is driven to 1 for all values of the temperature (coupling constant). For models recently proposed by K. R. Ito, where Migdal's and Kadanoff's recursion relations hold exactly, a lower bound on the string tension is derived. The results obtained by us extend those derived by Ito for U(1). Our method is based on analytic continuation of the Gibbs factors, which are class functions, in the central angles.