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| -rw-r--r-- | frsb_kac-rice.tex | 28 |
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diff --git a/figs/316_complexity.pdf b/figs/316_complexity.pdf Binary files differindex 081be84..2928239 100644 --- a/figs/316_complexity.pdf +++ b/figs/316_complexity.pdf diff --git a/figs/316_complexity_contour_1.pdf b/figs/316_complexity_contour_1.pdf Binary files differindex aabaf42..2bf7dc5 100644 --- a/figs/316_complexity_contour_1.pdf +++ b/figs/316_complexity_contour_1.pdf diff --git a/figs/316_complexity_contour_2.pdf b/figs/316_complexity_contour_2.pdf Binary files differindex 4521ced..837c12e 100644 --- a/figs/316_complexity_contour_2.pdf +++ b/figs/316_complexity_contour_2.pdf diff --git a/figs/316_complexity_contour_leg.pdf b/figs/316_complexity_contour_leg.pdf Binary files differindex 4e381de..ac19156 100644 --- a/figs/316_complexity_contour_leg.pdf +++ b/figs/316_complexity_contour_leg.pdf diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index a1ac0c1..130b7e9 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -887,8 +887,7 @@ become dominant over minima at a higher energy $E_\mathrm{th}=-1.287\,575\,114\l The 1RSB complexity transitions to a RS description for dominant stationary points at an energy $E_1=-1.273\,886\,852\ldots$. The highest energy for which the 1RSB description exists is $E_\mathrm{max}=-0.886\,029\,051\ldots$ -All these complexities can be seen plotted in -Fig.~\ref{fig:2rsb.complexity}. +The complexity along interesting trajectories is plotted in Fig.~\ref{fig:2rsb.complexity}. @@ -907,9 +906,11 @@ Fig.~\ref{fig:2rsb.complexity}. \begin{figure} \centering + \hspace{-1em} \includegraphics{figs/316_complexity_contour_1.pdf} + \hspace{-1em} \includegraphics{figs/316_complexity_contour_2.pdf} - \raisebox{4em}{\includegraphics{figs/316_complexity_contour_leg.pdf}} + \raisebox{3em}{\includegraphics{figs/316_complexity_contour_leg.pdf}} \caption{ Complexity of the $3+16$ model in the energy $E$ and stability $\mu$ @@ -927,13 +928,20 @@ Fig.~\ref{fig:2rsb.complexity}. \includegraphics{figs/316_detail.pdf} \caption{ - Complexity of the $3+16$ model in the energy $E$ and stability $\mu$ - plane. The right shows a detail of the left. The black line shows $\mu_m$, - which separates minima above from saddles below. The white lines show the - dominant stationary points at each energy, dashed when they are described - by a RS solution and solid for 1RSB. The red line shows the transition - between RS and 1RSB descriptions. The gray line shows where the RS - description predicts zero complexity. + Detail of the `phases' of the $3+16$ model complexity as a function of + energy and stability. Above the yellow marginal stability line the + complexity counts saddles of fixed index, while below that line it counts + minima of fixed stability. The shaded red region shows places where the + complexity is described by the 1RSB solution, while the shaded gray region + shows places where the complexity is described by the RS solution. In white + regions the complexity is zero. Several interesting energies are marked + with vertical black lines: the traditional `threshold' $E_\mathrm{th}$ + where minima become most numerous, the algorithmic threshold + $E_\mathrm{alg}$ that bounds the performance of smooth algorithms, and the + average energies at the $2$RSB and $1$RSB equilibrium transitions $\langle + E\rangle_2$ and $\langle E\rangle_1$, respectively. Though the figure is + suggestive, $E_\mathrm{alg}$ lies slightly below the termination of the RS + -- 1RSB transition line. } \end{figure} |