Entropy barriers and slow relaxation in some random walk models

We study the zero temperature limit of a simple model of slow relaxation without energy barriers, recently proposed by Ritort, as well as two other closely related models with a much faster relaxation. These models can be mapped onto random walk problems, which allows for their analytic study. We analyse, in particular, a specific aspect of the former model, namely the existence of a bias leading to 'entropy barriers' and to a very slow relaxation.