analysed to estimate the locations of critical points, and the values of critical exponents and scaling of adsorbing walks, in the square and cubic lattices. The algorithm is related to the Rosenbluth algorithm [@RR55] and to the GARM algoritm [@RJvR08]. The GARM algorithm is related to the PERM algorithm [@G97; @HG11], and flat histogram implementations of PERM [@PK04] have been used to sample states from a flat histogram over state space in a variety of different models of interacting walks, including collapsing walks [@PO00] and adsorbing walks [@KPOL04].

figure1-.tex

The GAS algorithm was introduced in reference [@JvRR09] and was used in several studies as an algorithm to approximately enumerate walks or polygons [@JvRR11; @JvRR11A]. However, it was not clear how to generalise the algorithm to sample states in models of interacting walks. In this paper our purpose is (1) to generalise the algorithm to a model of adsorbing walks, (2) to examine the behaviour of the algorithm by computing critical points and exponents of the walk, and to compare this to results found elsewhere, and (3) to use our data to examine scaling in adsorbing walks by computing critical exponents and examining the scaling of thermodynamic functions.

Adsorbing walks {#subsection1.2}
