On the absence of ferromagnetism in typical 2D ferromagnets

Details On the absence of ferromagnetism in typical 2D ferromagnets On the absence of ferromagnetism in typical 2D ferromagnets

2006-08-03

arxiv.org/abs/math-ph/0608009v3

Commun. Math. Phys. 274 (2007), no. 1, 217-231

Physics

Mathematical Physics

15 pages, CMP style file

Scientific paper

10.1007/s00220-007-0260-0

We consider the Ising systems in $d$ dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions which decay with a 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 $d\ge2$) magnetic order can occur.

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