Effective field theory for He-IV

We introduce an effective scalar field theory to describe the He-IV phase diagram, which can be considered as a generalization of the XY model which gives the usual lambda-transition. This theory results from a Ginzburg-Landau Hamiltonian with higher order derivatives, which allow to produce transitions between the superfluid, normal liquid and solid phases of He-IV. Mean field and Monte Carlo analyses suggest that this model is able to reproduce the main qualitative features of He-IV phase transitions.