Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimization of the dynamic transition in the continuous coloring
  problem   Random constraint satisfaction problems can exhibit a phase where the number
of constraints per variable $\alpha$ makes the system solvable in theory on the
one hand, but also makes the search for a solution hard, meaning that common
algorithms such as Monte-Carlo method fail to find a solution. The onset of
this hardness is deeply linked to the appearance of a dynamical phase
transition where the phase space of the problem breaks into an exponential
number of clusters. The exact position of this dynamical phase transition is
not universal with respect to the details of the Hamiltonian one chooses to
represent a given problem. In this paper, we develop some theoretical tools in
order to find a systematic way to build a Hamiltonian that maximizes the
dynamic $\alpha_{\rm d}$ threshold. To illustrate our techniques, we will
concentrate on the problem of continuous coloring, where one tries to set an
angle $x_i \in [0;2\pi]$ on each node of a network in such a way that no
adjacent nodes are closer than some threshold angle $\theta$, that is $\cos(x_i
- x_j) \leq \cos\theta$. This problem can be both seen as a continuous version
of the discrete graph coloring problem or as a one-dimensional version of the
the Mari-Krzakala-Kurchan (MKK) model. The relevance of this model stems from
the fact that continuous constraint satisfaction problems on sparse random
graphs remain largely unexplored in statistical physics. We show that for
sufficiently small angle $\theta$ this model presents a random first order
transition and compute the dynamical, condensation and Kesten-Stigum
transitions; we also compare the analytical predictions with Monte Carlo
simulations for values of $\theta = 2\pi/q$, $q \in \mathbb{N}$. Choosing such
values of $q$ allows us to easily compare our results with the renowned problem
of discrete coloring.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex