  We consider scaling of the mean square dipole moments in a plasma with
logarithmic interactions in a two- and three-dimensional system. In both cases,
we establish the existence of a low-temperature regime where the mean square
dipole moment does not scale with system size and a high-temperature regime
where it does scale with system size. Thus, there is a nonanalytic change in
the polarizability of the system as a function of temperature, and hence a
metal-insulator transition in both cases. The relevance of this transition in
three dimensions to quantum phase transitions in 2+1-dimensional systems is
briefly discussed.
