Abstract
We introduce an effective scalar field theory to describe the $^{4}\mathrm{He}$ phase diagram, which can be considered as a generalization of the $XY$ model which gives the usual $\ensuremath{\lambda}$ transition. This theory results from a Ginzburg-Landau Hamiltonian with higher order derivatives, which allow one to produce transitions between the superfluid, normal liquid, and solid phases of $^{4}\mathrm{He}$. Mean field and Monte Carlo analyses suggest that this model is able to reproduce the main qualitative features of $^{4}\mathrm{He}$ phase transitions.
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