York University, Toronto, Ontario M3J 1P3, Canada\'
author:
- 'E.J. Janse van Rensburg$^1$'
bibliography:
- 'References.bib'
title: 'Microcanonical Simulations of Adsorbing Self-Avoiding Walks'
---

Introduction {#section1}
============

The adsorption of a linear polymer on an attractive surface is a conformational rearrangement of the polymer to a state where it explores conformations which remain near or on the surface. This is the so-called polymer adsorption transition, and the many models of this phenomenon (see, for example, reference [@JvR15]) remain a rich source of mathematical and numerical studies. Polymer adsorption is a phase transition [@BDG83], and the properties of the adsorbed polymer have been examined both experimentally (see, for example, references [@DR71; @BDD95; @MBM14]) and theoretically [@deG79]. These models include directed path models of adsorbing polymers [@PFF88; @W98], as well as self-avoiding walk models [@HTW82], and these have received considerable attention in the literature [@HG94], using both rigorous methods [@RW11] and numerical methods (for example, the Monte Carlo simulation of adsorbing self-avoiding walks [@JvRR04]).

In this study, a new Monte Carlo method for sampling adsorbing self-avoiding walks is proposed and implemented. In particular, the GAS algorithm [@JvRR09] is generalised to sample adsorbing walks in the microcanonical ensemble, and the data obtained are 