[12] Monte-Carlo cluster algorithm for ferromagnetic Hamiltonians $H=J\sum_{(ij)}(S_{i}.S_{j})^3$

We prove by Monte-Carlo simulations that the cubic term in the Hamiltonian $H=J\sum_{(ij)}{\bf S}_{i}.{\bf S}_{j}+({\bf S}_{i}.{\bf S}_{j})^3$ is irrelevant for the critical behavior as predicted by the Renormalization group.