Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean field dilute ferromagnet I. High temperature and zero temperature
  behavior   We study the mean field dilute model of a ferromagnet. We find and prove an
expression for the free energy density at high temperature, and at temperature
zero. We find the critical line of the model, separating the phase with zero
magnetization from the phase with symmetry breaking. We also compute exactly
the entropy at temperature zero, which is strictly positive. The physical
behavior at temperature zero is very interesting and related to infinite
dimensional percolation, and suggests possible behaviors at generic low
temperatures. Lastly, we provide a complete solution for the annealed model.
Our results hold both for the Poisson and the Bernoulli versions of the model.

20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg