  One way of making the transition between the quasi-long range order in a
chain of S=1/2 spins coupled antiferromagnetically and the true long range
order that occurs in a plane, is by assembling chains to make ladders of
increasing width. Surprisingly this crossover between one and two dimensions is
not at all smooth. Ladders with an even number of legs have purely short range
magnetic order and a finite energy gap to all magnetic excitations. Predictions
of this novel groundstate have now been verified experimentally. Holes doped
into these ladders are predicted to pair, and possibly superconduct.
