  Machine learning methods are powerful in distinguishing different phases of
matter in an automated way and provide a new perspective on the study of
physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data
constructed with spin configurations sampled from the Ising Hamiltonian at
different values of temperature and external magnetic field using Monte Carlo
methods. From the trained machine we obtain the flow of iterative
reconstruction of spin state configurations to faithfully reproduce the
observables of the physical system. We find that the flow of the trained RBM
approaches the spin configurations of the maximal possible specific heat which
resemble the near criticality region of the Ising model. In the special case of
the vanishing magnetic field the trained RBM converges to the critical point of
the Renormalization Group (RG) flow of the lattice model. Our results suggest
an alternative explanation of how the machine identifies the physical phase
transitions, by recognizing certain properties of the configuration like the
maximization of the specific heat, instead of associating directly the
recognition procedure with the RG flow and its fixed points. Then from the
reconstructed data we deduce the critical exponent associated to the
magnetization to find satisfactory agreement with the actual physical value. We
assume no prior knowledge about the criticality of the system and its
Hamiltonian.
