  Contours associated to many interesting low-temperature statistical mechanics
models (2D Ising model, (2+1)D SOS interface model, etc) can be described as
self-interacting and self-avoiding walks on $\mathbb Z^2$. When the model is
defined in a finite box, the presence of the boundary induces an interaction,
that can turn out to be attractive, between the contour and the boundary of the
box. On the other hand, the contour cannot cross the boundary, so it feels
entropic repulsion from it. In various situations of interest a crucial
technical problem is to prove that entropic repulsion prevails over the pinning
interaction: in particular, the contour-boundary interaction should not modify
significantly the contour partition function and the related surface tension
should be unchanged. Here we prove that this is indeed the case, at least at
sufficiently low temperature, in a quite general framework that applies in
particular to the models of interest mentioned above.
