Supermultiplicative relations in models of interacting self-avoiding walks and polygons

Abstract

Fekete’s lemma shows the existence of limits in subadditive sequences. This lemma, and generalisations of it, also have been used to prove the existence of thermodynamic limits in statistical mechanics. In this paper it is shown that the two variable supermultiplicative relation together with mild assumptions, imply the existence of the limit This is a generalisation of Fekete’s lemma. The existence of is proven for models of adsorbing walks and polygons, and for pulled polygons. In addition, numerical data are presented estimating the general shape of of models of square lattice self-avoiding walks and polygons.