From 18353a6c1d3b5e95c7e585ab968db5b6e27ebcd8 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 12 Jul 2022 14:08:45 +0200 Subject: Added cartoon. --- figs/cartoon_1RSB.pdf | Bin 0 -> 59948 bytes figs/cartoon_2RSB.pdf | Bin 0 -> 51325 bytes figs/cartoon_RS.pdf | Bin 0 -> 41376 bytes frsb_kac-rice.tex | 22 ++++++++++++++++++++++ 4 files changed, 22 insertions(+) create mode 100644 figs/cartoon_1RSB.pdf create mode 100644 figs/cartoon_2RSB.pdf create mode 100644 figs/cartoon_RS.pdf diff --git a/figs/cartoon_1RSB.pdf b/figs/cartoon_1RSB.pdf new file mode 100644 index 0000000..ed3eef6 Binary files /dev/null and b/figs/cartoon_1RSB.pdf differ diff --git a/figs/cartoon_2RSB.pdf b/figs/cartoon_2RSB.pdf new file mode 100644 index 0000000..2246150 Binary files /dev/null and b/figs/cartoon_2RSB.pdf differ diff --git a/figs/cartoon_RS.pdf b/figs/cartoon_RS.pdf new file mode 100644 index 0000000..af0c523 Binary files /dev/null and b/figs/cartoon_RS.pdf differ diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index e42046d..c5641a4 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -1261,6 +1261,28 @@ draw two stationary points from the same set with nonzero probability. Therefore, the picture in this case is of few, large basins each containing exponentially many stationary points. +\begin{figure} + \centering + \includegraphics{figs/cartoon_RS.pdf} + \hfill + \includegraphics{figs/cartoon_1RSB.pdf} + \hfill + \includegraphics{figs/cartoon_2RSB.pdf} + + \caption{ + A cartoon visualizing how to interpret replica symmetry breaking solutions + in the complexity. The black region show schematically areas where + stationary points of a given energy can be found. Left: When the region + is connected, pairs of stationary points exist at any overlap, but the + vast majority of pairs are orthogonal. Center: When there are exponentially + many disconnected regions of similar size, the vast majority of pairs will + be found in different, orthogonal regions. Right: When there are a few + large disconnected regions, pairs have a comparable probability to be found + in different regions or in the same region. This gives rise to two (or + more) possible overlaps. + } \label{fig:cartoon} +\end{figure} + \subsection{A concrete example} One can construct a schematic 2RSB model from two 1RSB models. -- cgit v1.2.3-70-g09d2