Long range order for lattice dipoles

Details Long range order for lattice dipoles Long range order for lattice dipoles

2008-03-25

arxiv.org/abs/0803.3576v1

Jour. Stat. Phys. 134, 1059-1070 (2009)

Physics

Mathematical Physics

9 pages

Scientific paper

10.1007/s10955-008-9596-x

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.

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