The present paper is dedicated to the investigation of a two-dimensional Bose system with the density-density type interparticle interaction. We showed the possibility of a finite temperature phase transition and investigated the Goldstone singularities for both homogeneous and vortex ground states. The critical exponents of the O (n > 1) symmetric Emptyset(4) model were computed within the epsilon-expansion for epsilon = 2. (C) 2018 The Author(s). Published by Elsevier B.V.