Knot probability of polygons subjected to a force: a Monte Carlo study

We use Monte Carlo methods to study the knot probability of lattice polygons on the cubic lattice in the presence of an external force f. The force is coupled to the span of the polygons along a lattice direction, say the z-direction. If the force is negative polygons are squeezed (the compressive regime), while positive forces tend to stretch the polygons along the z-direction (the tensile regime). For sufficiently large positive forces we verify that the Pincus scaling law in the force-extension curve holds. At a fixed number of edges n the knot probability is a decreasing function of the force. For a fixed force the knot probability approaches unity as 1 - exp(-alpha(0)(f)n + o(n)), where alpha(0)(f) is positive and a decreasing function of f. We also examine the average of the absolute value of the writhe and we verify the square root growth law (known for f = 0) for all values of f