  This article analyzes the decoherence induced on a single qubit by the
interaction with a spin chain with nontrivial internal dynamics (XY-type
interactions). The aim of the paper is to study the existence and properties of
the so-called universal regime, in which the decoherence time scale becomes
independent of the strength of the coupling with the environment. It is shown
that although such regime does exist, as previously established by Cucchietti
\textit{et al} in {\em Phys. Rev. A}, 75:032337 (2007), it is not a clear
signature of a quantum phase transition in the environment. In fact, this kind
of universality also exists in the absence of quantum phase transitions. A
universal regime can be related to the existence of an energy scale separation
between the Hamiltonian of the environment and the one characterizing the
system-environment interaction. The results presented also indicate that in the
strong coupling regime the quantum phase transition does not produce an
enhancement of decoherence (as opposed to what happens in the weak coupling
regime).
