Loop models with crossings
by Andrea Bedini
Abstract: The universal behaviour of two-dimensional loop models changes dramatically when loops are allowed to cross. In the polymer limit of zero loop fugacity, the model of self-avoiding trails (walks which are bond-avoiding but not necessarily site-avoiding) has been studied numerically for years without much progress on the theoretical understanding of its universality properties. Only recently, a description of its continuum limit in terms of the non-linear sigma model on the real projective space has been proposed.