  The monolayer of $\textrm{CrI}_3$ has been reported to exhibit the
ferromagnetic order, with a Curie temperature of $45 K$ and off-plane easy
axis, which has attracted much attention in the community of condensed matter
physics. Using the Density Matrix Renormalization Group method, we investigate
the role of correlation effects and using classical Monte Carlo simulations
analyze the nature of phase transitions in the XXZ Hamiltonian on a honeycomb
lattice, which can effectively model $\textrm{CrI}_3$. We show, that the
magnetic ordering of the Hamiltonian's ground state can be well approximated by
classical models in a wide range of an anisotropy parameter space. Using
classical Monte Carlo simulations we estimate the Curie temperature of $49.7 K$
which is in good agreement with experimental result.
