On the absence of ferromagnetism in typical 2D ferromagnets

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 $d\ge 2$) magnetic order can occur.

15 pages, CMP style file

References in corpus (2)

• Ising models with long-range dipolar and short-range ferromagnetic interactions
• Frustrated phase separation in two-dimensional charged systems

Cited by in corpus (12)

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• Stripe-tetragonal phase transition in the 2D Ising model with dipole interactions: Partition-function zeros approach
• Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions
• One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures
• Formation of stripes and slabs near the ferromagnetic transition
• Stability of ground state degeneracy to long-range interactions
• Multidimensional Contours à la Fröhlich-Spencer and Boundary Conditions for Quantum Spin Systems
• Absence of magnetism in continuous-spin systems with long-range antialigning forces