Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A hierarchical mean field model of interacting spins   We consider a system of hierarchical interacting spins under dynamics of
spin-flip type with a ferromagnetic mean field interaction, scaling with the
hierarchical distance, coupled with a system of linearly interacting
hierarchical diffusions of Ornstein-Uhlenbeck type. In particular, the
diffusive variables enter in the spin-flip rates, effectively acting as
dynamical magnetic fields. In absence of the diffusions, the spin-flip dynamics
can be thought of as a modification of the Curie--Weiss model. We study the
mean field and the two-level hierarchical model, in the latter case restricting
to a subcritical regime, corresponding to high temperatures, obtaining
macroscopic limits at different spatio-temporal scales and studying the phase
transitions in the system. We also formulate a generalization of our results to
the $k$-th level hierarchical case, for any $k$ finite, in the subcritical
regime. We finally address the supercritical regime, in the zero-temperature
limit, for the two-level hierarchical case, proceeding heuristically with the
support of numerics.

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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con