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@@ -1845,6 +1845,17 @@ gapped minima are unlikely to see Stokes lines. } \label{fig:numeric.angle.gap} \end{figure} +We can also see that as the empirical gap is increased, Stokes points tend to +occur at very large phases. This can be seen for $N=32$ in +Fig.~\ref{fig:numeric.angle.gap}, which shows the probability distribution of +Stokes lines discovered as a function of phase $|\theta|$ necessary to reach +them. The curves are broken into sets representing different bins of the +empirical gap $|\lambda_\textrm{min}|$. As the empirical gap grows, Stokes +points become depleted around small phases and concentrate on very large ones. +This supports the idea that around the gapped minima, Stokes points will be +concentrated at phases that are nearly $180^\circ$, where the two-replica +calculation shows that almost all of their nearest neighbors will lie. + \subsection{Pure {\it p}-spin: is analytic continuation possible?} After this work, one is motivated to ask: can analytic continuation be done in |