  Accessibility percolation is a new type of percolation problem inspired by
evolutionary biology: a random number, called its fitness, is assigned to each
vertex of a graph, then a path in the graph is accessible if fitnesses are
strictly increasing through it. In the Rough Mount Fuji (RMF) model the fitness
function is defined on the graph as $\omega(v)=\eta(v)+\theta\cdot d(v)$, where
$\theta$ is a positive number called the drift, $d$ is the distance to the
source of the graph and $\eta(v)$ are i.i.d. random variables. In this paper we
determine values of $\theta$ for having RMF accessibility percolation on the
hypercube and the two-dimensional lattices $\mathbb{L}^2$ and
$\mathbb{L}^2_{alt}$.
