  We investigate how thermal quantum discord (QD) and classical correlations
(CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium
depend on the temperature of the bath as well as on nonuniform external
magnetic fields applied to two qubits and varied separately. We show that the
behavior of QD differs in many unexpected ways from the thermal entanglement
(EOF). For the nonuniform case (B1 = -B2), we find that QD and CC are equal for
all values of (B1 = -B2) and for different temperatures. We show that, in this
case, the thermal states of the system belong to a class of mixed states and
satisfy certain conditions under which QD and CC are equal. The specification
of this class and the corresponding conditions are completely general and apply
to any quantum system in a state in this class satisfying these conditions. We
further find that the relative contributions of QD and CC can be controlled
easily by changing the relative magnitudes of B1 and B2. Finally, we connect
our results with the monogamy relations between the EOF, CC and the QD of two
qubits and the environment.
