Abstract
We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur.
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Communicated by M. Aizenman
© 2007 by M. Biskup, L. Chayes and S.A. Kivelson. Reproduction, by any means, of the entire article for non-commercial purposes is permitted without charge.
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Biskup, M., Chayes, L. & Kivelson, S.A. On the Absence of Ferromagnetism in Typical 2D Ferromagnets. Commun. Math. Phys. 274, 217–231 (2007). https://doi.org/10.1007/s00220-007-0260-0
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DOI: https://doi.org/10.1007/s00220-007-0260-0