  Considering an example of the long-range Kitaev model, we are looking for a
correlation length in a model with long range interactions whose correlation
functions away from a critical point have power-law tails instead of the usual
exponential decay. It turns out that quasiparticle spectrum depends on a
distance from the critical point in a way that allows to identify the standard
correlation length exponent, $\nu$. The exponent implicitly defines a
correlation length $\xi$ that diverges when the critical point is approached.
We show that the correlation length manifests itself also in the correlation
function but not in its exponential tail because there is none. Instead $\xi$
is a distance that marks a crossover between two different algebraic decays
with different exponents. At distances shorter than $\xi$ the correlator decays
with the same power law as at the critical point while at distances longer than
$\xi$ it decays faster, with a steeper power law. For this correlator it is
possible to formulate the usual scaling hypothesis with $\xi$ playing the role
of the scaling distance. The correlation length also leaves its mark on the
subleading anomalous fermionic correlator but, interestingly, there is a regime
of long range interactions where its short distance critical power-law decay is
steeper than its long distance power law tail.
