  Using the monomer-dimer representation of strongly coupled U(N) lattice gauge
theories with staggered fermions, we study finite temperature chiral phase
transitions in (2+1) dimensions. A new cluster algorithm allows us to compute
monomer-monomer and dimer-dimer correlations at zero monomer density (chiral
limit) accurately on large lattices. This makes it possible to show
convincingly, for the first time, that these models undergo a finite
temperature phase transition which belongs to the Kosterlitz-Thouless
universality class. We find that this universality class is unaffected even in
the large N limit. This shows that the mean field analysis often used in this
limit breaks down in the critical region.
