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The statistical mechanics of single polymer knots is studied using MonteCarlo simulations. The polymers are considered on a cubic lattice and theirconformations are randomly changed with the help of pivot transformations.After each transformation, it is checked if the topology of the knot ispreserved by means of a method called pivot algorithm and excluded area (inshort PAEA) and described in a previous publication of the authors. As anapplication of this method the specific energy, the radius of gyration and heatcapacity of a few types of knots are computed. The case of attractiveshort-range forces is investigated. The sampling of the energy states isperformed by means of the Wang-Landau algorithm. The obtained results show thatthe specific energy and heat capacity increase with increasing knot complexityas in the case of repulsive interactions. The data about the gyration radiusallow to estimate the size of the polymer knots at different temperatures.

A numerical technique for preserving the topology of polymer knots: The case of short-range attractive interactions