  We describe an approach to understanding exponential decay of correlation
functions in asymptotically free theories. This approach is systematic; it does
not start from any conjectured mechanism or picture. We begin by studying the
metric on the space of configurations and the behavior of the potential-energy
function on this space.
  We describe how these ideas fit in the framework of QCD, as discussed earlier
by one of us (P.O.). We then consider the 1+1-dimensional O(2) and O(3)
nonlinear sigma models and show that no gap exists in the former at weak
coupling. In the O(3) model a new kind of strong/weak-coupling duality is
realized. We briefly outline our proposals for understanding the spectrum.
