Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Phase Transition in a Quenched Amorphous Ferromagnet   Quenched thermodynamic states of an amorphous ferromagnet are studied. The
magnet is a countable collection of point particles chaotically distributed
over $\mathbb{R}^d$, $d\geq 2$. Each particle bears a real-valued spin with
symmetric a priori distribution; the spin-spin interaction is pair-wise and
attractive. Two spins are supposed to interact if they are neighbors in the
graph defined by a homogeneous Poisson point process. For this model, we prove
that with probability one: (a) quenched thermodynamic states exist; (b) they
are multiple if the particle density (i.e., the intensity of the underlying
point process) and the inverse temperature are big enough; (c) there exist
multiple quenched thermodynamic states which depend on the realizations of the
underlying point process in a measurable way.

28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics