THE NONLINEAR SIGMA-MODEL AND SPIN LADDERS

The well known Haldane map from spin chains into the O(3) nonlinear si gma model is generalized to the case of spin ladders. This map allows us to explain the different qualitative behaviour between even and odd ladders, in exactly the same way as it explains the difference betwee n integer and half-integer spin chains. Namely, for even ladders the t opological term in the sigma model action is absent, while for odd lad ders the theta parameter, which multiplies the topological term, is eq ual to 2 pi S, where S is the spin of the ladder. Hence even ladders s hould have a dynamically generated spin gap, while odd ladders with ha lf-integer spin should stay gapless and physically equivalent to a per turbed SU(2)(1) Wess-Zumino-Witten model in the infrared regime. We al so derive some consequences from the dependence of the sigma model cou pling constant on the ladder Heisenberg couplings constants.