  We consider the problem of quantum and classical phase transitions in
double-layer quantum Hall systems at $\nu=1/m$ (m odd integers) from a
long-wavelength statistical mechanics viewpoint. We derive an explicit mapping
of the long-wavelength Lagrangian of the quantum Hall system into that of a
three-dimensional isotropic classical XY model whose coupling constant depends
on the quantum fluctuation in the original quantum Hall Hamiltonian. Universal
properties of the quantum phase transition at the critical layer separation are
completely determined by this mapping. The dependence of the
Kosterlitz-Thouless transition temperature on layer separation, including
quantum fluctuation effects, is approximately obtained by simple finite-size
scaling analyses.
