  This is an edited version of an unpublished 1979 EFI (U. Chicago) preprint:
"The U(N) lattice gauge theory in 2-dimensions can be considered as the
statistical mechanics of a Coulomb gas on a circle in a constant electric
field. The large N limit of this system is discussed and compared with exact
answers for finite N. Near the fixed points of the renormalization group and
especially in the critical region where one can define a continuum theory,
computations in the thermodynamic limit $(N \rightarrow \infty)$ are in
remarkable agreement with those for finite and small N. However, in the
intermediate coupling region the thermodynamic computation, unlike the one for
finite N, shows a continuous phase transition. This transition seems to be a
pathology of the infinite N limit and in this simple model has no bearing on
the physical continuum limit."
