Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theories of Matter: Infinities and Renormalization   This paper looks at the theory underlying the science of materials from the
perspectives of physics, the history of science, and the philosophy of science.
We are particularly concerned with the development of understanding of the
thermodynamic phases of matter. The question is how can matter, ordinary
matter, support a diversity of forms. We see this diversity each time we
observe ice in contact with liquid water or see water vapor (steam) rise from a
pot of heated water. The nature of the phases is brought into the sharpest
focus in phase transitions: abrupt changes from one phase to another and hence
changes from one behavior to another. This article starts with the development
of mean field theory as a basis for a partial understanding of phase transition
phenomena. It then goes on to the limitations of mean field theory and the
development of very different supplementary understanding through the
renormalization group concept.
  Throughout, the behavior at the phase transition is illuminated by an
"extended singularity theorem", which says that a sharp phase transition only
occurs in the presence of some sort of infinity in the statistical system. The
usual infinity is in the system size. Apparently this result caused some
confusion at a 1937 meeting celebrating van der Waals, since mean field theory
does not respect this theorem. In contrast, renormalization theories can make
use of the theorem. This possibility, in fact, accounts for some of the
strengths of renormalization methods in dealing with phase transitions. The
paper outlines the different ways phase transition phenomena reflect the
effects of this theorem.

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int