Discrete spin cubic model on a fractal lattice - the ground state phase diagram

We study the ground state properties of the discrete spin cubic model situated on the Sierpinski gasket fractal lattice. The relevant model Hamiltonian contains exchange and quadrupolar interaction terms, associated with the parameters J1 and J2, respectively. We have found that the model under study has a very rich ground state diagram in the (J1,J2)-plane, with one ordered (ferromagnetic) state and three regions of different frustrated states.