Zero-point vacancies in the two-dimensional t-J2-J3-J4 model: 3He on graphite surface

We consider dynamics of zero-point vacancies introduced in the two-dimensional (2D) solid 3He adsorbed on a graphite surface. We thereby propose an improved model, i.e., t-J2-J3-J4 model, which takes into account the proper truncation of the ring-exchange paths in the presence of the vacancies. We find that, in contrast to the t-J-K model, the doping of vacancies makes the system less ferromagnetic in consistent with experiment and thus the improved model is essential for understanding the magnetic-field dependence of the system.