Metal-insulator transition in two- and three-dimensional logarithmic plasmas

We consider the scaling of the mean square dipole moment in a plasma with logarithmic interactions in a two- and three-dimensional systems. 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.