  We study the finite temperature crossovers in the vicinity of a zero
temperature quantum phase transition. The universal crossover functions are
observables of a continuum quantum field theory. Particular attention is
focussed on the high temperature limit of the continuum field theory, the
so-called ``quantum-critical'' region. Basic features of crossovers are
illustrated by a simple solvable model of dilute spinless fermions, and a
partially solvable model of dilute bosons. The low frequency relaxational
behavior of the quantum-critical region is displayed in the solution of the
transverse-field Ising model. The insights from these simple models lead to a
fairly complete understanding of the system of primary interest: the
two-dimensional quantum rotor model, whose phase transition is expected to be
in the same universality class as those in antiferromagnetic Heisenberg spin
models. Recent work on the experimental implications of these results for the
cuprate compounds is briefly reviewed.
