Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of fluctuations on the Geodesic rule for topological defect
  formation   At finite temperature, the field along a linear stretch of correlation length
size is supposed to trace shortest path in the field space given the two end
points, known as the Geodesic rule. In this study we compute the probability
that the field variations over distances of correlation length follow the
Geodesic rule in theories with $O(2)$ global symmetry. We consider a model of
ferromagnetic $O(2)$ spins and a complex $\phi^4$ theory. The computations are
carried out on an ensemble of equilibrium configurations at finite temperatures
generated using Monte Carlo simulations. The numerical results suggest that,
for temperatures relevant for the studies of topological defect formation
during 2nd order phase transition, there is a significant deviation from the
Geodesic rule. We also study the equilibrium density and distribution of
vortices in O(2) spins in two dimensions and compare with the Kibble-Zurek
Mechanism of defect formation.

32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin