Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hysteresis and complexity in the zero-temperature mean-field RFIM: the
  soft-spin version   We study the energy landscape of the soft-spin random field model in the
mean-field limit and compute analytically the quenched complexity of the
metastable states as a function of their magnetization and energy at a given
external magnetic field. The shape of the domain within which the complexity is
positive (and the number of typical metastable states grows exponentially with
system size) changes with the amount of disorder and becomes non-convex and
disconnected at low disorder. As a consequence, phase transitions occur both at
equilibrium and out of equilibrium along the saturation hysteresis loop. We
focus on the zero complexity curve in the field-magnetization plane and its
relationship with the hysteresis loop. We also study the response of the system
when the magnetization is externally controlled instead of the magnetic field.
The main features of the model that should survive in finite dimensions are
discussed.

2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess