  In answer to the replies of Reslen {\it et al} [arXiv: quant-ph/0507164
(2005)], and Liberti and Zaffino [arXiv:cond-mat/0507019, (2005)], we comment
once more on the temperature-dependent effective Hamiltonians for the Dicke
model derived by them in [Europhys. Lett., {\bf 69} (2005) 8] and [Eur. Phys.
J., {\bf 44} (2005) 535], respectively. These approximate Hamiltonians cannot
be correct for any finite nonzero temperature because they both violate a
rigorous result. The fact that the Dicke model belongs to the universality
class of, and its thermodynamics is described by the infinitely coordinated
transverse-field XY model is known for more than 30 years.
