  Quantum discord is a function of density-matrix elements (and through them,
e.~g., of temperature, applied fields, time, and so forth).
  The domain of such a function in the case of two-qubit system with X or
centrosymmetric (CS) density matrix can consist at most of three subdomains:
two ones, where the quantum discord is expressed in closed analytical forms
(Q_0 and Q_{\pi/2}), and an intermediate subdomain in which for determining the
quantum discord Q_\theta it is required to solve numerically a one-dimensional
minimization problem to find the optimal measurement angle \theta\in(0,\pi/2).
Exact equations for determining the boundaries between these subdomains are
obtained and solved for a number of models. The Q_\theta subdomains are
discovered in the anisotropic spin dimers in external field.
  On the other hand, coinciding boundaries and therefore sudden transitions
between optimal measurement angles \theta=\pi/2 and \theta=0 are observed in
dynamics of spin currying particles in closed nanopore and also in phase flip
channels. In latter cases the solutions are entirely analytical.
