2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/21392We investigate the probability for appearance of knots in self-avoiding loops (SALs) on a cubic lattice. A set of N-step loops is generated by attempting to combine pairs of (N/2)-step self-avoiding walks constructed by a dimerization method. We demonstrate that our method produces unbiased samples of SALs, and study the knot formation probability as a function of loop size. Our results corroborate the conclusions of Yao et. al. with loops generated by a Monte Carlo method.RevTeX4, 4 pages, 4 eps figuresStatistical MechanicsSoft Condensed Mattertext