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 Fröhlich 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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Dedicated to Jürg Fröhlich and Thomas Spencer on the occasion of their 60th birthday.
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Giuliani, A. Long Range Order for Lattice Dipoles. J Stat Phys 134, 1059–1070 (2009). https://doi.org/10.1007/s10955-008-9596-x
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DOI: https://doi.org/10.1007/s10955-008-9596-x