Two-dimensional Gibbsian point processes with continuous spin symmetries

The conservation of continuous symmetries in two-dimensional systems with interaction is a classical subject of statistical mechanics. So far, all results of this sort required some smoothness properties of the interaction. Only recently Ioffe et al. (Comm. Math. Phys. 226 (2002) 433) succeeded to treat the case of lattice systems with continuous, rather than smooth, interaction. Here we establish a similar result for Gibbsian systems of point particles with internal degrees of freedom.