Comment on equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

Brankov, J. G.; Tonchev, N. S.; Zagrebnov, V. A.

Comment on equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

Authors

Brankov, J. G.

Tonchev, N. S.

Zagrebnov, V. A.

Description

In this Comment we show that the temperature-dependent effective Hamiltonian derived by Reslen {\it et al} [Europhys. Lett., {\bf 69} (2005) 8] or that one by Liberti and Zaffino [arXiv:cond-mat/0503742] for the Dicke model cannot be correct for any temperature. They both violate a rigorous result. The former is correct only in the quantum (zero-temperature) limit while the last one only in the classical (infinite temperature) limit. The fact that the Dicke model belongs to the universality class of the infinitely coordinated transverse-field XY model is known for more then 30 years.
5 pages, no figures