Singular interaction potentials in classical statistical mechanics

A classical system of particles interacting through a stable two-body potential ts considered. It is shown that for a certain class of stable, essentially singular potentials and sufficiently large value of the cutoff parameter the stability property of the potential is preserved. It is shown that the thermodynamic potentials (pressure, free energy density) and the correlation functions are asymptotically independent of the continuation of the potential in the neighborhood of the singularity.