06-228 Marek Biskup, Lincoln Chayes, Steven A. Kivelson
On the absence of ferromagnetism in typical 2D ferromagnets (144K, PDF) Aug 21, 06
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Abstract. 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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