Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamic Limit for the Ising Model on the Cayley Tree   While the Ising model on the Cayley tree has no spontaneous magnetization at
nonzero temperatures in the thermodynamic limit, we show that finite systems of
astronomical sizes remain magnetically ordered in a wide temperature range, if
the symmetry is broken by fixing an arbitrary single (bulk or surface) spin. We
compare the behavior of the finite size magnetization of this model with that
of the Ising model on both the Sierpinski Gasket, and the one-dimensional
linear chain. This comparison reveals the analogy of the behavior of the
present model with the Sierpinski Gasket case.

25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys