Interacting Loop Ensembles and Bose Gases

We study interacting Bose gases in thermal equilibrium on a lattice. establish convergence of the grand-canonical Gibbs states such to their mean-field (classical field) and large-mass particle) limits. The former is classical field theory for complex scalar with quartic self-interaction. latter point particles two-body interactions. Our analysis based representations terms ensembles random loops, Ginibre loop ensemble Symanzik theories. For small enough interactions, our results also hold infinite volume. this paper were previously sketched Fröhlich et al. (J Stat Phys 180(1–6):810–831, 2020).