$g$, where the miscible phase exists in the lower region. Full numerical results are in black, while the analytical prediction \[Eq. (\[Eq:gc\])\] is blue (gray). The vertical dashed lines represent the three interaction strengths that are the focus throughout the paper, i.e. $g = \{4, 8, 500\}$. Inset: magnification of the region where the immiscibility boundary begins to significantly rise above the thermodynamic-limit result $g_{12}^{\rm c,TD}/g=1$. \[Fig:PhaseD\]](Fig3){width="3.3in"}

The immiscibility boundary is summarized by a phase diagram in Fig. \[Fig:PhaseD\], with the numerical result in black and the variational one in blue (gray). For large $g$, the boundary levels off to the thermodynamic-limit prediction $g_{12}^{\rm c,TD}/g=1$. At the other extreme, where $g$ becomes small, the size of the miscible region grows as the role of quantum pressure increases and acts to stabilize the mixed phase. The small-$g$ regime is precisely where the variational model is appropriate. This explains why it captures the increasing trend of $g_{12}^{\rm c}/g$, yet the curve is qualitatively accurate throughout the region of parameters used.

Enhanced Quantum Spin Fluctuations {#Sec:ResultsSF}
----------------------------------

![Spin $S_{\mathcal{S}}(k_x,k_y=0,\omega)$ and density $S_{\mathcal{D}}(k_x,k_y=0,\omega)$ dynamic structure factor for the case of (a-b) uncoupled condensates ($g_{12}=0$), and (c-d) balanced intercomponent and intracomponent interactions ($g_{12}/g=1$), where $g 