  We consider a semiflexible polymer in $\mathbb Z^d$ which is a random
interface model with a mixed gradient and Laplacian interaction. The strength
of the two operators is governed by two parameters called lateral tension and
bending rigidity, which might depend on the size of the graph. In this article
we show a phase transition in the scaling limit according to the strength of
these parameters: we prove that the scaling limit is, respectively, the
Gaussian free field, a "mixed" random distribution and the continuum membrane
model in three different regimes.
