A low temperature expansion and “spin wave picture” for classical N-vector models

Abstract

We obtain a convergent multi-scale expansion for a class of low temperature classical vector spin models, of the type of lattice “λ|φ|4” field theory, in dimensions d ≥ 3. With the help of this expansion we prove main statements of the so called “spin wave picture”, like the existence of a continuum of phases parametrized by vectors of the unit sphere in the space of spins φ, and the existence of Goldstone bosons, i.e. free massless decay of truncated transversal two-point correlation functions.