Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loop-erased random walk as a spin system observable   The determination of the Hausdorff dimension of the scaling limit of
loop-erased random walk is closely related to the study of the one-point
function of loop-erased random walk, i.e., the probability a loop-erased random
walk passes through a given vertex. Recent work in the theoretical physics
literature has investigated the Hausdorff dimension of loop-erased random walk
in three dimensions by applying field theory techniques to study spin systems
that heuristically encode the one-point function of loop-erased random walk.
Inspired by this, we introduce two different spin systems whose correlation
functions can be rigorously shown to encode the one-point function of
loop-erased random walk.

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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th