Self-avoiding random loops versus Ising model in three dimensions

On the basis of a recently developed lattice model for ensembles of random loops which contains a parameter interpolating between self-avoiding and Ising-like loops, we calculate the average length and the length fluctuations of self-avoiding loops in three dimensions, using analytic as well as Monte Carlo methods, and compare the results with the Ising case. Applying finite-size scaling techniques, we show that the critical behavior of self-avoiding random loops is consistent with universality predictions based on the Ising model.