We determine the critical couplings for the deconfinement phase transition in SU (2) gauge theory on N τ × N 3 σ lattices with N τ = 8 and 16 and N σ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio T c / √ σ in the entire coupling regime β = 2.30 − 2.75, while the individual quantities still exhibit large scaling violations. We find T c / √ σ =0.69(2). We also discuss in detail the extrapolation of T c /Λ MS and √ σ/Λ MS to the continuum limit. Our result, which is consistent with the above ratio, is T c /Λ MS = 1.23(11) and √ σ/Λ MS = 1.79(12). We also comment upon corresponding results for SU (3) gauge theory and four flavour QCD.

We present results of a detailed investigation of the temperature dependence of the spatial string tension in SU(2) gauge theory. We show, for the first time, that the spatial string tension is scaling on the lattice and thus is nonvanishing in the continuum limit. It is temperature independent below T c and rises rapidly above. For temperatures larger than 2T C we find a scaling behavior consistent with cr s (T) = (0.136 ± 0.011)# 4 (T)T 2 , where g(T) is the two-loop running coupling constant with a scale parameter determined as AT = (0.076 =b 0.013)T C .