Estimating partition function using Montecarlo methods

While working on a completely unrelated quantum computing problem, I ran into a quantity that can be mapped to a partition function of spins on a triangular lattice. It is not quite an Ising model, though, since interaction happens between triplets of spins, some configurations are not allowed, and I don’t explicitly have the Hamiltonian but only the weight of every configuration (I guess one could just pick a random value for the temperature and define a Hamiltonian, but it would probably just be a more complicated mess).

I have been trying to understand if I can use Montecarlo methods to get the partition function, but I am getting lost in the literature. From what I understood, my best shot would be to use something like the Wang-Landau algorithm to estimate the density of states and use that to get the partition function, but I couldn’t find any paper detailing such a procedure so if someone could give me some good literature to look at (or any suggestions) that would be very helpful.

Thanks!

P.S. As far as I understand, Wang-Landau gives the density of states up to a normalization constant. However, in my specific case I have some conditions on this fictitious "partition function" that should allow me to infer that constant.