Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Random Field Induced Ordering in the Classical XY Model   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.

8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom