On the roughening transition in non-abelian lattice gauge theories

We estimate the location βsub(R) = (g2sub(R)N)-1 of the recently discussed roughening transition for SU(N) lattice gauge theories in ν = 3 and 4 dimensions. The obtained values always lie in the crossover region where the string tension starts to deviate significantly from the leading strong coupling behaviour. βsub(R)(N) increases as N increases, tending to a finite limit (approx.0.38 for ν = 4) as N → infinite. Results for the solid on solid model (SOS) approximation are also presented and shown to give a good qualitative description; however, group theoretical effects seem to be important for quantitative estimates. (orig.)