Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A renormalisation group method. III. Perturbative analysis   This paper is the third in a series devoted to the development of a rigorous
renormalisation group method for lattice field theories involving boson fields,
fermion fields, or both. In this paper, we motivate and present a general
approach towards second-order perturbative renormalisation, and apply it to a
specific supersymmetric field theory which represents the continuous-time
weakly self-avoiding walk on $\mathbb{Z}^d$. Our focus is on the critical
dimension $d=4$. The results include the derivation of the perturbative flow of
the coupling constants, with accompanying estimates on the coefficients in the
flow. These are essential results for subsequent application to the
4-dimensional weakly self-avoiding walk, including a proof of existence of
logarithmic corrections to their critical scaling. With minor modifications,
our results also apply to the 4-dimensional $n$-component $|\varphi|^4$ spin
model.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc