  The transverse-field XY model in one dimension is a well-known spin model for
which the ground state properties and excitation spectrum are known exactly.
The model has an interesting phase diagram describing quantum phase transitions
(QPTs) belonging to two different universality classes. These are the
transverse-field Ising model and the XX model universality classes with both
the models being special cases of the transverse-field XY model. In recent
years, quantities related to quantum information theoretic measures like
entanglement, quantum discord (QD) and fidelity have been shown to provide
signatures of QPTs. Another interesting issue is that of decoherence to which a
quantum system is subjected due to its interaction, represented by a quantum
channel, with an environment. In this paper, we determine the dynamics of
different types of correlations present in a quantum system, namely, the mutual
information, the classical correlations and the quantum correlations, as
measured by the quantum discord, in a two-qubit state. The density matrix of
this state is given by the nearest-neighbour reduced density matrix obtained
from the ground state of the transverse-field XY model in 1d. We assume
Markovian dynamics for the time-evolution due to system-environment
interactions. The quantum channels considered include the bit-flip,
bit-phase-flip and phase-flip channels. Two different types of dynamics are
identified for the channels in one of which the quantum correlations are
greater in magnitude than the classical correlations in a finite time interval.
The origins of the different types of dynamics are further explained. For the
different channels, appropriate quantities associated with the dynamics of the
correlations are identified which provide signatures of QPTs. We also report
results for further-neighbour two-qubit states and finite temperatures.
