per site indicates a factorizing field, in this case the simple polarized state. This factorizing field is discussed further below in the context of the more general $XYX$ model.

In contrast to the previous models studied here, the GE is not maximal at the phase transition point, because the phase transition point is not the critical point which would correspond to maximum entanglement. In this case zero or nonzero GE per site distinguishes between the two different phases in the model.

![(color online) Plots for the 2D spin-$\frac12$ XXX model with varying magnetic field $h$. (a) Local magnetization $m$ for sublattices A and B, obtained with iPEPS truncation dimension $D=2$. (b) Amplitude of the local order parameters $M$. (c) GE per site ${\mathcal E}(h)$. []{data-label="fig3"}](delta10a.eps "fig:"){width="0.8\linewidth"} ![(color online) Plots for the 2D spin-$\frac12$ XXX model with varying magnetic field $h$. (a) Local magnetization $m$ for sublattices A and B, obtained with iPEPS truncation dimension $D=2$. (b) Amplitude of the local order parameters $M$. (c) GE per site ${\mathcal E}(h)$. []{data-label="fig3"}](delta10b.eps "fig:"){width="0.8\linewidth"} ![(color online) Plots for the 2D spin-$\frac12$ XXX model with varying magnetic field $h$. (a) Local magnetization $m$ for sublattices A and B, obtained with iPEPS truncation dimension $D=2$. 