Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical computation of the magnetization probability density function
  for the harmonic 2D XY model   The probability density function (PDF) of some global average quantity plays
a fundamental role in critical and highly correlated systems. We explicitly
compute this quantity as a function of the magnetization for the two
dimensional XY model in its harmonic approximation. Numerical simulations and
perturbative results have shown a Gumbel-like shape of the PDF, in spite of the
fact that the average magnetization is not an extreme variable. Our analytical
result allows to test both perturbative analytical expansions and also
numerical computations performed previously. Perfect agreement is found for the
first moments of the PDF. Also for large volume and in the high temperature
limit the distribution becomes Gaussian, as it should be. In the low
temperature regime its numerical evaluation is compatible with a Gumbel
distribution.

14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat