Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization Group Transformations Near the Critical Point: Some
  Rigorous Results   We consider renormalization group (RG) transformations for classical
Ising-type lattice spin systems in the infinite volume limit. Formally, the RG
maps a Hamiltonian H into a renormalized Hamiltonian H':
exp(-H'(\sigma'))=\sum_\sigma T(\sigma, \sigma')exp(-H(\sigma)), where
T(\sigma, \sigma') denotes a specific RG probability kernel, \sum_\sigma'
T(\sigma, \sigma')=1, for every configuration \sigma. With the help of the
Dobrushin uniqueness condition and standard results on the polymer expansion,
Haller and Kennedy gave a sufficient condition for the existence of the
renormalized Hamiltonian in a neighborhood of the critical point. By a more
complicated but reasonably straightforward application of the cluster expansion
machinery, the present investigation shows that their condition would further
imply a band structure on the matrix of partial derivatives of the renormalized
interaction with respect to the original interaction. This in turn gives an
upper bound for the RG linearization.

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The categories of this paper are: cs
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas