Self-avoiding walk, spin systems, and renormalisation

Gordon Slade

Published 2018-08-13Version 1

The self-avoiding walk, and lattice spin systems such as the $\varphi^4$ model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical exponents. We survey some of these problems, and report on recent advances in their mathematical understanding via a rigorous nonperturbative renormalisation group method.