Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical Droplets and sharp asymptotics for Kawasaki dynamics with
  strongly anisotropic interactions   In this paper we analyze metastability and nucleation in the context of the
Kawasaki dynamics for the two-dimensional Ising lattice gas at very low
temperature. Let $\Lambda\subset\mathbb{Z}^2$ be a finite box. Particles
perform simple exclusion on $\Lambda$, but when they occupy neighboring sites
they feel a binding energy $-U_1<0$ in the horizontal direction and $-U_2<0$ in
the vertical one. Thus the Kawasaki dynamics is conservative inside the volume
$\Lambda$. Along each bond touching the boundary of $\Lambda$ from the outside
to the inside, particles are created with rate $\rho=e^{-\Delta\beta}$, while
along each bond from the inside to the outside, particles are annihilated with
rate $1$, where $\beta>0$ is the inverse temperature and $\Delta>0$ is an
activity parameter. Thus, the boundary of $\Lambda$ plays the role of an
infinite gas reservoir with density $\rho$. We consider the parameter regime
$U_1>2U_2$ also known as the strongly anisotropic regime. We take
$\Delta\in{(U_1,U_1+U_2)}$, so that the empty (respectively full) configuration
is a metastable (respectively stable) configuration. We investigate how the
transition from empty to full takes place with particular attention to the
critical configurations that asymptotically have to be crossed with probability
1. The derivation of some geometrical properties of the saddles allows us to
identify the full geometry of the minimal gates and their boundaries for the
nucleation in the strongly anisotropic case. We observe very different
behaviors for this case with respect to the isotropic ($U_1=U_2$) and weakly
anisotropic ($U_1<2U_2$) ones. Moreover, we derive mixing time, spectral gap
and sharp estimates for the asymptotic transition time for the strongly
anisotropic case.

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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ