Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical Solution of Classical Magnetic Models with Long-Range
  Couplings   We study the canonical solution of a family of classical $n-vector$ spin
models on a generic $d$-dimensional lattice; the couplings between two spins
decay as the inverse of their distance raised to the power $\alpha$, with
$\alpha<d$. The control of the thermodynamic limit requires the introduction of
a rescaling factor in the potential energy, which makes the model extensive but
not additive. A detailed analysis of the asymptotic spectral properties of the
matrix of couplings was necessary to justify the saddle point method applied to
the integration of functions depending on a diverging number of variables. The
properties of a class of functions related to the modified Bessel functions had
to be investigated. For given $n$, and for any $\alpha$, $d$ and lattice
geometry, the solution is equivalent to that of the $\alpha=0$ model, where the
dimensionality $d$ and the geometry of the lattice are irrelevant.

19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th