magnetic field as control parameter. In this easy-plane region the model is known to undergo a continuous quantum phase transition in the same universality class as the transverse Ising model [@tros]. The GE was seen to have a cusp at the critical value $h_c$ [@gehlw; @hl] as observed for the transverse Ising model (recall Fig. \[fig1\](b)). Significantly, it is known that a factorizing field exists at the value $h_f = 2 \sqrt{2(1+\Delta_y)}$, with $h_f < h_c$, where the ground state becomes a separable product state [@tros]. At this point it follows that the GE vanishes, i.e., ${\mathcal E}_{\infty}(h_f) = 0$. This was observed in the simulations using GE [@gehlw; @hl]. Other entanglement measures were also confirmed to vanish at this point [@tros; @lsh].

In this study we consider the fixed parameter value $h=0.25$ and vary the coupling $\Delta_{y}$. The model is anticipated to undergo a transition at $\Delta_{y}=1$ from an antiferromagnetic phase in the $x$ direction to an antiferromagnetic phase in the $y$ direction, with local order parameter the staggered magnetization $M_x$ ($M_y$) corresponding to the phase $\Delta_{y}<1$ ($\Delta_{y}>1$).

![(color online) Plots for the spin-$\frac12$ XYX model with fixed magnetic field $h=0.25$ and varying anisotropy parameter $\Delta_y$. (a) Components of 