  The statistical mechanics of single polymer knots is studied using Monte
Carlo simulations. The polymers are considered on a cubic lattice and their
conformations are randomly changed with the help of pivot transformations.
After each transformation, it is checked if the topology of the knot is
preserved by means of a method called pivot algorithm and excluded area (in
short PAEA) and described in a previous publication of the authors. As an
application of this method the specific energy, the radius of gyration and heat
capacity of a few types of knots are computed. The case of attractive
short-range forces is investigated. The sampling of the energy states is
performed by means of the Wang-Landau algorithm. The obtained results show that
the specific energy and heat capacity increase with increasing knot complexity
as in the case of repulsive interactions. The data about the gyration radius
allow to estimate the size of the polymer knots at different temperatures.
