Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of dynamics, Lyapunov exponents and phase transitions   The Hamiltonian dynamics of classical planar Heisenberg model is numerically
investigated in two and three dimensions. By considering the dynamics as a
geodesic flow on a suitable Riemannian manifold, it is possible to analytically
estimate the largest Lyapunov exponent in terms of some curvature fluctuations.
The agreement between numerical and analytical values for Lyapunov exponents is
very good in a wide range of temperatures. Moreover, in the three dimensional
case, in correspondence with the second order phase transition, the curvature
fluctuations exibit a singular behaviour which is reproduced in an abstract
geometric model suggesting that the phase transition might correspond to a
change in the topology of the manifold whose geodesics are the motions of the
system.

37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin