  Recently, it has been proposed that the adsorption transition for a single
polymer in dilute solution, modeled by lattice walks in three dimensions, is
not universal with respect to inter-monomer interactions. It has also been
conjectured that key critical exponents $\phi$, measuring the growth of the
contacts with the surface at the adsorption point, and $1/\delta$, which
measures the finite-size shift of the critical temperature, are not the same.
However, applying standard scaling arguments the two key critical exponents
should be identical, thus pointing to a potential breakdown of these standard
scaling arguments. This is in contrast to the well studied situation in two
dimensions, where there are exact results from conformal field theory: these
exponents are both accepted to be $1/2$ and universal. We use the flatPERM
algorithm to simulate self-avoiding walks and trails on the hexagonal, square
and simple cubic lattices up to length $1024$ to investigate these claims.
Walks can be seen as a repulsive limit of inter-monomer interaction for trails,
allowing us to probe the universality of adsorption. For each model we analyze
several thermodynamic properties to produce different methods of estimating the
critical temperature and the key exponents. We test our methodology on the
two-dimensional cases and the resulting spread in values for $\phi$ and
$1/\delta$ indicates that there is a systematic error that exceeds the
statistical error usually reported. We further suggest a methodology for
consistent estimation of the key adsorption exponents which gives
$\phi=1/\delta=0.484(4)$ in three dimensions. We conclude that in three
dimensions these critical exponents indeed differ from the mean-field value of
$1/2$, but cannot find evidence that they differ from each other. Importantly,
we also find no substantive evidence of any non-universality in the polymer
adsorption transition.
