  Sudden changes of quantum correlations in the Bell-diagonal states are
well-known effects. They occur when the set of optimal parameters that
determine the quantum correlation consists of isolated points and optimal
parameters during the evolution of the system jump from one such point to
another (e.g., the optimal measurement angle of the quantum discord changes
discontinuously from zero to $\pi/2$ or vice versa). However, when considering
more general X quantum states, we found that quantum discord and one-way
quantum work deficit can experience sudden changes of other kinds. Namely, the
optimal measurement angle may suddenly start to shift {\em continuously} from
its stationary value 0 or $\pi/2$ to an intermediate optimal measurement angle
$\vartheta\in(0,\pi/2)$. This leads to a new behavior of quantum correlations,
which is mathematically described by the Landau phenomenological theory of
second-order phase transitions. In addition, for the one-way quantum work
deficit, we found cases where the optimal measurement angle jumps from zero to
a nonzero step less than $\pi/2$, and then continuously changes its value. This
behavior of quantum correlation is similar to a first-order phase transition in
Landau's theory. Dependencies of quantum discord and one-way quantum work
deficit near the boundaries, which separate regions with state-dependent
(variable) and state-independent (stationary, constant) optimal measurement
angles, are examined in detail on an example of the XXZ spin model in an
external field at thermal equilibrium.
