Motivated by the experimental findings and the available recent theoretical works of two-dimensional van der Waals ferromagnets, we calculated the critical coupling strength of \(\hbox {VI}_{3}\) and \(\hbox {CrI}_{3}\) monolayers. We expressed the monolayer Hamiltonian as pairwise interactions with the Ising model and analyzed the problem with the renormalization group theory. We used the decimation transformation method while applying the renormalization group theory. Using the methods we developed earlier, we overcame the problem of the decimated lattice not being self-dual. Since the \(\hbox {CrI}_{3}\) and \(\hbox {VI}_{3}\) lattice structures are the same, the coupling constants \(K_{\rm m,c}\) corresponding to these monolayers were calculated as 0.383; here index m denotes either \(\hbox {CrI}_{3}\) or \(\hbox {VI}_{3}\) . Since the experimentally determined critical temperatures of these monolayers are also very close to each other, the exchange coupling energy \(J_{\rm m,c}\) corresponding to these monolayers was determined approximately as \(3.2\times 10^{-22}\) Joule.
