Alpha matter on a lattice

We obtain the equation of state of interacting alpha matter and the critical temperature of Bose-Einstein condensation of alpha particles within an effective scalar field theory. We start from a non-relativistic model of uniform alpha matter interacting with attractive two-body and repulsive three-body potentials and reformulate this model as a O(2) symmetric scalar \phi^6 field theory with negative quartic and positive sextic interactions. Upon restricting the Matsubara sums, near the temperature of Bose-Einstein condensation, to the zeroth order modes we further obtain an effective classical theory in three spatial dimensions. The phase diagram of the alpha matter is obtained from simulations of this effective field theory on a lattice using local Monte-Carlo algorithms.