\[tc\]\[tc\][$(J-J_c)/r$]{} \[bc\]\[bc\][$|\mathcal{C}|$]{} ![ Plots of $|\mathcal{C}|$ for varying lengths of the spin chain, ranging from $N=3$ to $N=11$ (odd numbers only). The longer the spin chain, the more sharply peaked is the graph. The number of vertices on the circuit is kept constant, at $\mathcal{N} = 100$. []{data-label="fig:varyspinnumber"}](abscnum100all "fig:"){width=".45\textwidth" height=".3\textwidth"}

An analogous plot is shown in Fig. \[fig:varypointnumber\], but this time for a fixed number of spins $N$ and a varying number of circuit vertices $\mathcal{N}$.

\[tc\]\[tc\][$(J-J_c)/r$]{} \[bc\]\[bc\][$|\mathcal{C}|$]{} \[tl\]\[tl\][$\mathcal{N} = 300$]{} \[tl\]\[tl\][$\mathcal{N} = 100$]{} ![ Plots of $|\mathcal{C}|$ for varying numbers of vertices on the circuit, ranging from $\mathcal{N}=100$ to $\mathcal{N}=300$ (in steps of $50$). The more vertices there are on the circuit, the more sharply peaked is the graph. The spin chain length is kept constant, at just $N = 3$. Note that qualitatively nothing changes as we increase the chain length (tested up to $N=13$). []{data-label="fig:varypointnumber"}](N3allabscnumA "fig:"){width=".45\textwidth" height=".3\textwidth"}

Of course, there is a perfectly plausible explanation for these results: as the circuit passes over the critical point the ground state changes abruptly, so that the overlap of the ground states on either side of the critical point will be rather small in magnitude. This in turn forces the 