  In this paper we investigate the multifractal decomposition of the limit set
of a finitely generated, free Fuchsian group with respect to the mean cusp
winding number. We will completely determine its multifractal spectrum by means
of a certain free energy function and show that the Hausdorff dimension of sets
consisting of limit points with the same scaling exponent coincides with the
Legendre transform of this free energy function. As a by-product we generalise
previously obtained results on the multifractal formalism for infinite iterated
function systems to the setting of infinite graph directed Markov systems.
