  In several physical systems, important properties characterizing the system
itself are theoretically related with specific degrees of freedom. Although
standard Monte Carlo simulations provide an effective tool to accurately
reconstruct the physical configurations of the system, they are unable to
isolate the different contributions corresponding to different degrees of
freedom. Here we show that unsupervised deep learning can become a valid
support to MC simulation, coupling useful insights in the phases detection task
with good reconstruction performance. As a testbed we consider the 2D XY model,
showing that a deep neural network based on variational autoencoders can detect
the continuous Kosterlitz-Thouless (KT) transitions, and that, if endowed with
the appropriate constrains, they generate configurations with meaningful
physical content.
