  In this paper we complete the study on the asymptotic behaviour of the
entanglement entropy for Kitaev chains with long range pairing. We discover
that when the couplings decay with the distance with a critical exponent new
properties for the asymptotic growth of the entropy appear. The coefficient of
the leading term is not universal any more and the connection with conformal
field theories is lost. We perform a numerical and analytical approach to the
problem showing a perfect agreement. In order to carry out the analytical
study, a new technique for computing the asymptotic behaviour of block Toeplitz
determinants with discontinuous symbols has been developed.
