Statistics of flexible rings with excluded volume

A grand partition function of a system of closed self-avoiding lines on a lattice is studied. The examples of such lines are closed linear singularities: dislocations, vortex lines, etc. The partition function is expressed in the form of an integral over fictitious fields so that the behaviour of the whole system and a single ring in the system may be qualitatively described. A length distribution of rings, a mean radius of a ring of length L in the system and an effective interaction of the points of a probe ring, arising from the interaction of the probe ring with other rings, have been derived. An impact of broken rings is discussed.