FM: 2007-08; arXiv:0803.3576

Author : Alessandro Giuliani

Title: Long range order for lattice dipoles

Abstract: We consider a system of classical Heisenberg spins on a cubic lattice in dimensions three or more, interacting via the dipole-dipole interaction. We prove that at low enough temperature the system displays orientational long range order, as expected by spin wave theory. The proof is based on reflection positivity methods. In particular, we demonstrate a previously unproven conjecture on the dispersion relation of the spin waves, first proposed by Froehlich and Spencer, which allows one to apply infrared bounds for estimating the long distance behavior of the spin-spin correlation functions.

Keywords: O(n) spin models; dipole interactions; reflection positivity; infrared bounds.

Alessandro Giuliani,
Dipartimento di Matematica,
Universita' di Roma Tre,
L.go S. Leonardo Murialdo 1, 00146 Roma, Italy