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| -rw-r--r-- | frsb_kac-rice.tex | 9 |
1 files changed, 4 insertions, 5 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index a7a03cc..3b17093 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -12,8 +12,7 @@ ]{hyperref} % ref and cite links with pretty colors \begin{document} -\title{Full solution of the Kac--Rice problem for mean-field models.\\ -or Full solution for the counting of saddles of mean-field glass models} +\title{Full solution for counting stationary points of mean-field complex energy landscapes} \author{Jaron Kent-Dobias \& Jorge Kurchan} \maketitle \begin{abstract} @@ -39,11 +38,11 @@ of small temperature for the lowest states, as it should. To understand the importance of this computation, consider the following situation. When one solves the problem of spheres in large dimensions, one finds that there is a transition at a given temperature to a one-step one step symmetry breaking (1RSB) phase at a Kauzmann temperature, and, at a lower temperature, -another transition to a full RSB phase (see \cite{gross1985mean,gardner1985spin}, the `Gardner ' phase \cite{charbonneau2014fractal}. +another transition to a full RSB phase (see \cite{Gross_1985_Mean-field, Gardner_1985_Spin}, the `Gardner ' phase \cite{Charbonneau_2014_Fractal}. Now, this transition involves the lowest, equilibrium states. Because they are obviously unreachable at any reasonable timescale, an often addressed question to ask is: what is the Gardner transition line for higher than equilibrium -energy-densities? (see, for a review \cite{berthier2019gardner}) For example, +energy-densities? (see, for a review \cite{Berthier_2019_Gardner}) For example, when studying `jamming' at zero temperature, the question is posed as to "on what side of the 1RSB-FRS transition are the high energy (or low density) states reachable dynamically. Posed in this way, such a question does not have @@ -1081,7 +1080,7 @@ The solution contains valuable geometric information that has yet to be extracted in all detail. 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 understanding of what happens in a low-temperature realistic jamming dynamics \cite{maimbourg2016solution}. +a clear understanding of what happens in a low-temperature realistic jamming dynamics \cite{Maimbourg_2016_Solution}. \paragraph{Funding information} J K-D and J K are supported by the Simons Foundation Grant No. 454943. |