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| -rw-r--r-- | frsb_kac-rice_letter.tex | 41 |
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diff --git a/figs/24_phases_letter.pdf b/figs/24_phases_letter.pdf Binary files differnew file mode 100644 index 0000000..366f49e --- /dev/null +++ b/figs/24_phases_letter.pdf diff --git a/figs/316_complexity_contour_1_letter.pdf b/figs/316_complexity_contour_1_letter.pdf Binary files differnew file mode 100644 index 0000000..b5aa80d --- /dev/null +++ b/figs/316_complexity_contour_1_letter.pdf diff --git a/figs/316_detail_letter.pdf b/figs/316_detail_letter.pdf Binary files differnew file mode 100644 index 0000000..4c33457 --- /dev/null +++ b/figs/316_detail_letter.pdf diff --git a/figs/316_detail_letter_legend.pdf b/figs/316_detail_letter_legend.pdf Binary files differnew file mode 100644 index 0000000..756a2c7 --- /dev/null +++ b/figs/316_detail_letter_legend.pdf diff --git a/frsb_kac-rice_letter.tex b/frsb_kac-rice_letter.tex index 801dc8e..5917167 100644 --- a/frsb_kac-rice_letter.tex +++ b/frsb_kac-rice_letter.tex @@ -1,5 +1,5 @@ -\documentclass[reprint,aps,prl,longbibliography]{revtex4-2} +\documentclass[reprint,aps,prl,longbibliography,floatfix]{revtex4-2} \usepackage[utf8]{inputenc} % why not type "Bézout" with unicode? \usepackage[T1]{fontenc} % vector fonts plz @@ -187,7 +187,22 @@ find the complexity everywhere. This is how the data in what follows was produce \begin{figure} \centering - \includegraphics[width=\columnwidth]{figs/316_detail.pdf} + \hspace{-1em} + \includegraphics[width=\columnwidth]{figs/316_complexity_contour_1_letter.pdf} + + \caption{ + Complexity of the $3+16$ model in the energy $E$ and stability $\mu^*$ + plane. The right shows a detail of the left. Below the yellow marginal line + the complexity counts saddles of increasing index as $\mu^*$ decreases. + Above the yellow marginal line the complexity counts minima of increasing + stability as $\mu^*$ increases. + } \label{fig:2rsb.contour} +\end{figure} + +\begin{figure} + \centering + \includegraphics[width=\columnwidth]{figs/316_detail_letter.pdf} + \includegraphics[width=\columnwidth]{figs/316_detail_letter_legend.pdf} \caption{ Detail of the `phases' of the $3+16$ model complexity as a function of @@ -275,7 +290,7 @@ model stall in a place where minima are exponentially subdominant. \begin{figure} \centering - \includegraphics[width=\columnwidth]{figs/24_phases.pdf} + \includegraphics[width=\columnwidth]{figs/24_phases_letter.pdf} \caption{ `Phases' of the complexity for the $2+4$ model in the energy $E$ and stability $\mu^*$ plane. The region shaded gray shows where the RS solution @@ -294,25 +309,9 @@ also studied before in equilibrium \cite{Crisanti_2004_Spherical, Crisanti_2006_ \end{equation} In the equilibrium solution, the transition temperature from RS to FRSB is $\beta_\infty=1$, with corresponding average energy $\langle E\rangle_\infty=-0.53125\ldots$. -Along the supersymmetric line, the FRSB solution can be found in full, exact -functional form. To treat the FRSB away from this line numerically, we resort to -finite $k$RSB approximations. Since we are not trying to find the actual -$k$RSB solution, but approximate the FRSB one, we drop the extremal condition -\eqref{eq:cond.x} for $x_1,\ldots,x_k$ and instead set -\begin{equation} - x_i=\left(\frac i{k+1}\right)x_\textrm{max} -\end{equation} -and extremize over $x_\textrm{max}$ alone. This dramatically simplifies the -equations that must be solved to find solutions. In the results that follow, a -20RSB approximation is used to trace the dominant saddles and marginal minima, while -a 5RSB approximation is used to trace the (much longer) boundaries of the -complexity. - -Fig.~\ref{fig:frsb.complexity} shows the complexity for this model as a -function of energy difference from the ground state for several notable -trajectories in the energy and stability plane. Fig.~\ref{fig:frsb.phases} +Fig.~\ref{fig:frsb.phases} shows these trajectories, along with the phase boundaries of the complexity in -this plane. Notably, the phase boundary predicted by \eqref{eq:mu.transition} +this plane. Notably, the phase boundary predicted by a perturbative expansion correctly predicts where all of the finite $k$RSB approximations terminate. Like the 1RSB model in the previous subsection, this phase boundary is oriented such that very few, low energy, minima are described by a FRSB solution, while |