The shapes of self-avoiding polygons with torsion

We consider self-avoiding polygons on the simple cubic lattice with a torsion fugacity. We use Monte Carlo methods to generate large samples as a function of the torsion fugacity and the number of edges in the polygon. Using these data we investigate the shapes of the polygons at large torsion fugacity and find evidence that the polygons have substantial helical character. In addition, we show that these polygons have induced writhe for any non-zero torsion fugacity, and that torsion and writhe are positively correlated.