A corner transfer matrix renormalisation group investigation of the vertex-interacting self-avoiding walk model

摘要

A recently introduced extension of the Corner Transfer Matrix RenormalisationGroup (CTMRG) method useful for the study of self-avoiding walk type models ispresented in detail and applied to a class of interacting self-avoiding walksdue to Bl\"ote and Nienhuis. This model displays two different types ofcollapse transition depending on model parameters. One is the standard$\theta$-point transition. The other is found to give rise to a first-ordercollapse transition despite being known to be in other respects critical.