Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology and Phase Transitions II. Theorem on a necessary relation   In this second paper, we prove a necessity Theorem about the topological
origin of phase transitions. We consider physical systems described by smooth
microscopic interaction potentials V_N(q), among N degrees of freedom, and the
associated family of configuration space submanifolds {M_v}_{v \in R}, with
M_v={q \in R^N | V_N(q) \leq v}. On the basis of an analytic relationship
between a suitably weighed sum of the Morse indexes of the manifolds {M_ v}_{v
\in R} and thermodynamic entropy, the Theorem states that any possible unbound
growth with N of one of the following derivatives of the configurational
entropy S^{(-)}(v)=(1/N) \log \int_{M_v} d^Nq, that is of |\partial^k
S^{(-)}(v)/\partial v^k|, for k=3,4, can be entailed only by the weighed sum of
Morse indexes.
  Since the unbound growth with N of one of these derivatives corresponds to
the occurrence of a first or of a second order phase transition, and since the
variation of the Morse indexes of a manifold is in one-to-one correspondence
with a change of its topology, the Main Theorem of the present paper states
that a phase transition necessarily stems from a topological transition in
configuration space. The proof of the Theorem given in the present paper cannot
be done without Main Theorem of paper I.

35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat