  We used the Transfer-Integral method to compute, with an uncertainty smaller
than 5%, the six fundamental characteristic exponents of two dynamical models
for DNA thermal denaturation and investigate the validity of the scaling laws.
Doubts concerning this point arise because the investigated systems (i) have a
divergent internal length, (ii) are described by a divergent order parameter,
(iii) are of dimension 1. We found that the assumption that the free energy can
be described by a single homogeneous function is robust, despite the divergence
of the order parameter, so that Rushbrooke's and Widom's identities are valid
relations. Josephson's identity is instead not satisfied. This is probably due
to the divergence of the internal length, which invalidates the assumption that
the correlation length is solely responsible for singular contributions to
thermodynamic quantities. Fisher's identity is even wronger. We showed that
this is due to the d=1 dimensionality and obtained an alternative law, which is
well satisfied at DNA thermal denaturation.
