Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Statistical Mechanics of the Self-Gravitating Gas: Equation of State
  and Fractal Dimension   We provide a complete picture of the self-gravitating non-relativistic gas at
thermal equilibrium using Monte Carlo simulations (MC), analytic mean field
methods (MF) and low density expansions. The system is shown to possess an
infinite volume limit, both in the canonical (CE) and in the microcanonical
ensemble (MCE) when N, V \to \infty, keeping N/ V^{1/3} fixed. We {\bf compute}
the equation of state (we do not assume it as is customary), the entropy, the
free energy, the chemical potential, the specific heats, the compressibilities,
the speed of sound and analyze their properties, signs and singularities. The
MF equation of state obeys a {\bf first order} non-linear differential equation
of Abel type. The MF gives an accurate picture in agreement with the MC
simulations both in the CE and MCE. The inhomogeneous particle distribution in
the ground state suggest a fractal distribution with Haussdorf dimension D with
D slowly decreasing with increasing density, 1 \lesssim D < 3.

26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys