Disorder, local order and asymptotic freedom in spin and lattice gauge theories

We examine some aspects of the confinement problem from the point of view of simple molecular field and spin wave concepts applied to lattice gauge theory. Our main endeavour is to discover the reasons for the absence of a deconfining phase transition in 4 dimensions. The essential point we make is that the mechanism responsible for eliminating the transition is deeply related to, not to say implied by, asymptotic freedom, which is the principal characteristic of the system at low temperatures and short wavelengths. Our analysis is built on the analogy of lattice gauge theories with 2-dimensional spin systems. (orig.)