  The persistence length of semiflexible polymers and one-dimensional fluid
membranes is obtained from the renormalization of their bending rigidity. The
renormalized bending rigidity is calculated using an exact real-space
functional renormalization group transformation based on a mapping to the
one-dimensional Heisenberg model. The renormalized bending rigidity vanishes
exponentially at large length scales and its asymptotic behaviour is used to
define the persistence length. For semiflexible polymers, our result agrees
with the persistence length obtained using the asymptotic behaviour of tangent
correlation functions. Our definition differs from the one commonly used for
fluid membranes, which is based on a perturbative renormalization of the
bending rigidity.
