diff options
Diffstat (limited to 'frsb_kac-rice.tex')
| -rw-r--r-- | frsb_kac-rice.tex | 28 |
1 files changed, 14 insertions, 14 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index f21864f..9afdf7c 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -41,8 +41,6 @@ breaking, and one with full replica symmetry breaking. \end{abstract} -\tableofcontents - \section{Introduction} The computation of the number of metastable states of mean field spin glasses @@ -999,8 +997,8 @@ replica symmetry breaking when minima or inherent states do not. \includegraphics[width=\textwidth]{316_complexity.pdf} \caption{ - Complexity of dominant saddles (blue), marginal minima (yellow), and - dominant minima (green) of the $3+16$ model. Solid lines show the result of + Complexity of dominant saddles, marginal minima, and + dominant minima of the $3+16$ model. Solid lines show the result of the 1RSB ansatz, while the dashed lines show that of a RS ansatz. The complexity of marginal minima is always below that of dominant critical points except at the black dot, where they are dominant. @@ -1018,9 +1016,9 @@ replica symmetry breaking when minima or inherent states do not. \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 + plane. The right shows a detail of the left. Below the horizontal marginal line the complexity counts saddles of increasing index as $\mu^*$ decreases. - Above the yellow marginal line the complexity counts minima of increasing + Above the horizontal marginal line the complexity counts minima of increasing stability as $\mu^*$ increases. } \label{fig:2rsb.contour} \end{figure} @@ -1049,10 +1047,11 @@ model stall in a place where minima are exponentially subdominant. \caption{ Detail of the `phases' of the $3+16$ model complexity as a function of - energy and stability. Above the yellow marginal stability line the + energy and stability. Above the horizontal 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 + minima of fixed stability. The shaded red region to the left of the + transition line shows places where the complexity is described by the 1RSB + solution, while the shaded gray region to the right of the transition line 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' $E_\mathrm{th}$ @@ -1060,8 +1059,8 @@ model stall in a place where minima are exponentially subdominant. $E_\mathrm{alg}$ 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 at slightly lower energy than the termination of the RS - -- 1RSB transition line. + suggestive, $E_\mathrm{alg}$ lies at slightly lower energy than the + termination of the RS -- 1RSB transition line. } \label{fig:2rsb.phases} \end{figure} @@ -1160,9 +1159,10 @@ insight into lower-energy symmetry breaking in more general contexts. \includegraphics[width=\textwidth]{24_phases.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 - is correct, while the region shaded red shows that where the FRSB solution - is correct. The white region shows where the complexity is zero. + stability $\mu^*$ plane. The region shaded gray to the right of the + transition line shows where the RS solution is correct, while the region + shaded red to the left of the transition line shows that where the FRSB + solution is correct. The white region shows where the complexity is zero. } \label{fig:frsb.phases} \end{figure} |