  The orthogonality time is examined for different initial states settings
interacting locally with different types of spin interaction:
  $XX$, Ising and anisotropic models. It is shown that, the number of
orthogonality increases, and consequently the time of orthogonality decreases
as the environment qubits increase. The shortest time of orthogonality is
displayed for the $XX$ chain model, while the largest time is shown for the
Ising model. The external field increases the numbers of orthogonality, while
Dzyaloshinsky-Moriya interaction decreases the time of orthogonality. The
initial state settings together with the external field has a significant
effect on decreasing/increasing the time of orthogonality
