DMRG and Monte Carlo studies of $\textrm{CrI}_3$ magnetic phases and the phase transition

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.