and metric quantities of adsorbing walks.

The model of adsorbing walks is defined in section \[subsection1.2\], and its partition function and free energy are discussed. The limiting free energy of this model exists, and its properties have been examined elsewhere [@HTW82]; see, for example, reference [@JvR15]. The basic scaling relations for the free energy, energy, and specific heat were introduced above, and the scaling of the partition function was briefly reviewed.

In section \[section2\] the GAS algorithm [@JvRR09] is reviewed and then generalised to interacting models. The algorithm normally has only one set of parameters (associated with the size of the walks), but it is shown here that introducing a second set of parameters (associated with the energy of the walks) can give an algorithm which samples effectively in both length and energy. It is shown that the algorithm can be tuned to give flat histogram sampling in the spirit of the PERM algorithm [@G97; @HG11] (but without using enrichment or pruning of states).

Numerical results for adsorbing walks are analysed in section \[section3\]. The location of the adsorption critical point is determined from the mean energy of adsorbing walks, giving $$a_c^+ =
\cases{
1.779 \pm 0.003, & \hbox{in the 