Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metastability for Glauber dynamics on random graphs   In this paper we study metastable behaviour at low temperature of Glauber
spin-flip dynamics on random graphs. We fix a large number of vertices and
randomly allocate edges according to the Configuration Model with a prescribed
degree distribution. Each vertex carries a spin that can point either up or
down. Each spin interacts with a positive magnetic field, while spins at
vertices that are connected by edges also interact with each other via a
ferromagnetic pair potential. We start from the configuration where all spins
point down, and allow spins to flip up or down according to a Metropolis
dynamics at positive temperature. We are interested in the time it takes the
system to reach the configuration where all spins point up. In order to achieve
this transition, the system needs to create a sufficiently large droplet of
up-spins, called critical droplet, which triggers the crossover.
  In the limit as the temperature tends to zero, and subject to a certain
\emph{key hypothesis} implying metastable behaviour, the average crossover time
follows the classical \emph{Arrhenius law}, with an exponent and a prefactor
that are controlled by the \emph{energy} and the \emph{entropy} of the critical
droplet. The crossover time divided by its average is exponentially
distributed. We study the scaling behaviour of the exponent as the number of
vertices tends to infinity, deriving upper and lower bounds. We also identify a
regime for the magnetic field and the pair potential in which the key
hypothesis is satisfied. The critical droplets, representing the saddle points
for the crossover, have a size that is of the order of the number of vertices.
This is because the random graphs generated by the Configuration Model are
expander graphs.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas