Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Structures of Cluster Spins for Ising Models   We discussed hierarchies and rescaling rule of the self similar
transformations in Ising models, and define a fractal dimension of an ordered
cluster, which minimum corresponds to a fixed point of the transformations. By
the fractal structures we divide the clusters into two types: irreducible and
reducible. A relationship of cluster spin with its coordination number and
fractal dimension is obtained.

12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con