From a5d3d0ef02965cfb37a57bfb4e4c4c402447598c Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 13 Jul 2022 13:04:56 +0200 Subject: Acronym clarification. --- frsb_kac-rice.tex | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 1a576a3..8b83ae4 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -113,11 +113,11 @@ complexity. In \S\ref{sec:supersymmetric} we write down the solution in a specific and limited regime, which is nonetheless helpful as it gives a foothold for numerically computing the complexity everywhere else. \S\ref{sec:frsb} explains aspects of the solution specific to the case of full -RSB, and derives the RS--FRSB transition line. \S\ref{sec:examples} details the -landscape topology of two example models: a $3+16$ model with a 2RSB ground -state and a 1RSB complexity, and a $2+4$ with a FRSB ground state and a FRSB -complexity. Finally \S\ref{sec:interpretation} provides some interpretation of -our results. +RSB, and derives the replica symmetric to full FRSB (RS--FRSB) transition line. +\S\ref{sec:examples} details the landscape topology of two example models: a +$3+16$ model with a 2RSB ground state and a 1RSB complexity, and a $2+4$ with a +FRSB ground state and a FRSB complexity. Finally \S\ref{sec:interpretation} +provides some interpretation of our results. \section{The model} \label{sec:model} @@ -1411,7 +1411,9 @@ saddles of random mean-field landscapes, including systems with many steps of RSB. For systems with full RSB, we find that minima are exponentially subdominant with respect to saddles at all energy densities above the ground state. The solution contains valuable geometric information that has yet to be -extracted in all detail, for example considering several copies of the system \cite{Cavagna_1997_Structure}, or the extension to complex variables \cite{Kent-Dobias_2021_Complex, Kent-Dobias_2022_Analytic}. +extracted in all detail, for example considering several copies of the system +\cite{Cavagna_1997_Structure}, or the extension to complex variables +\cite{Kent-Dobias_2021_Complex, Kent-Dobias_2022_Analytic}. A first and very important application of the method here is to perform the calculation for high dimensional spheres, where it would give us a clear -- cgit v1.2.3-70-g09d2