On Random Field Induced Ordering in the Classical XY Model

Details On Random Field Induced Ordering in the Classical XY Model On Random Field Induced Ordering in the Classical XY Model

2010-09-26

arxiv.org/abs/1009.5068v1

Physics

Mathematical Physics

30 pages

Scientific paper

Consider the classical XY model in a weak random external field pointing along the $Y$ axis with strength $\epsilon$. We study the behavior of this model as the range of the interaction is varied. We prove that in any dimension $d \geq 2$ and for all $\epsilon$ sufficiently small, there is a range $L=L(\epsilon)$ so that whenever the inverse temperature $\beta$ is larger than some $\beta(\epsilon)$, there is strong residual ordering along the $X$ direction.

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