be represented by a normalizable solution, we tune the initial condition at the horizon so that the non-normalizable component vanishes. Figure \[fig:ads5Eh\] describes numerical solutions for $\tau=0.35$. The left graph shows the amplitude $h(r_+)=h_0$ at the horizon as a function of the momentum $k$.

Since there is a family of solutions parametrized by the momentum $k$, we need to choose the minimum energy density solution as the final state. The energy density is given as a sum of the electric and magnetic energy $$\mathcal H=\frac 1 {2\alpha^2} \int dr \left[ f'(r)^2 + \frac{k^2}{r^4} h(r)^2 + \frac{H(r)}{r^2} h'(r)^2\right]\;.$$ It is convenient to rescale the energy density as $\tilde{ \mathcal H} = \alpha^2 r_+^4 \mathcal H$, which is finite in the limit of $\alpha \rightarrow \infty$. The right graph of Figure \[fig:ads5Eh\] shows the energy density as a function of $k$. Choosing the momentum corresponding to the minimum of the energy density, the expectation value of the order parameter $|\left<J_3 + i J_4\right>|$ can be read off from the asymptotic behavior of the corresponding bulk field $h(r)$. Figure \[fig:TvsO\] shows the expectation value $|\left<J_3 + i J_4\right>|$ as a function of the rescaled temperature $\tau$. Near the critical temperature, it behaves as 