Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spontaneous collective synchronization in the Kuramoto model with
  additional non-local interactions   In the context of the celebrated Kuramoto model of globally-coupled phase
oscillators of distributed natural frequencies, which serves as a paradigm to
investigate spontaneous collective synchronization in many-body interacting
systems, we report on a very rich phase diagram in presence of thermal noise
and an additional non-local interaction on a one-dimensional periodic lattice.
Remarkably, the phase diagram involves both equilibrium and non-equilibrium
phase transitions. In two contrasting limits of the dynamics, we obtain exact
analytical results for the phase transitions. These two limits correspond to
(i) the absence of thermal noise, when the dynamics reduces to that of a
non-linear dynamical system, and (ii) the oscillators having the same natural
frequency, when the dynamics becomes that of a statistical system in contact
with a heat bath and relaxing to a statistical equilibrium state. In the former
case, our exact analysis is based on the use of the so-called Ott-Antonsen
ansatz to derive a reduced set of nonlinear partial differential equations for
the macroscopic evolution of the system. Our results for the case of
statistical equilibrium are on the other hand obtained by extending the
well-known transfer matrix approach for nearest-neighbor Ising model to
consider non-local interactions. The work offers a case study of exact analysis
in many-body interacting systems. The results obtained underline the crucial
role of additional non-local interactions in either destroying or enhancing the
possibility of observing synchrony in mean-field systems exhibiting spontaneous
synchronization.

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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat