Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero-temperature dynamics in the dilute Curie-Weiss model   We consider the Ising model on a dense Erd\H{o}s--R\'enyi random graph,
$\mathcal G(N,p)$, with $p>0$ fixed---equivalently, a disordered Curie--Weiss
Ising model with $\mbox{Ber}(p)$ couplings---at zero temperature. The disorder
may induce local energy minima in addition to the two uniform ground states. In
this paper we prove that, starting from a typical initial configuration, the
zero-temperature dynamics avoids all such local minima and absorbs into a
predetermined one of the two uniform ground states. We relate this to the local
MINCUT problem on dense random graphs; namely with high probability, the greedy
search for a local MINCUT of $\mathcal G(N,p)$ with $p>0$ fixed, started from a
uniform random partition, fails to find a non-trivial cut. In contrast, in the
disordered Curie--Weiss model with heavy-tailed couplings, we demonstrate that
zero-temperature dynamics has positive probability of absorbing in a random
local minimum different from the two homogenous ground states.

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The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-alg