Eq.(37) is solved self-consistently and the solutions are used to
determine the critical point Dc. At zero temperature, a spin–spin
correlation between nearest neighboring spins isfinite for DoDc
(the ordered phase) and abruptly vanishes when Dtends to Dc
,characterizing the quantum phase transition. In the large-D region,
the correlation ξ is null and the system falls into a disordered regime.
The critical points are numerically evaluated and the results are
shown in Fig. 9.