Distribution of instanton sizes in a simplified instanton gas model

We investigate the distribution of instanton sizes in the framework of a si mplified model for ensembles of instantons, This model takes into account t he non-diluteness of instantons. The infrared problem for the integration o ver instanton sizes is dealt with in a self-consistent manner by approximat ing instanton interactions by a repulsive hard core potential. This leads t o a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Mon te: Carlo methods. In one dimension exact results can be derived. In ang di mension we find a power law behaviour for small sizes, consistent with the semi-classical results. At large instanton sizes the distribution decays ex ponentially. The results are compared with those from lattice simulations.