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diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 6fbe0fb..873f9ae 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -84,13 +84,16 @@ Liao_2019_Hierarchical, Dennis_2020_Jamming, Charbonneau_2015_Numerical, Li_2021_Determining, Seguin_2016_Experimental, Geirhos_2018_Johari-Goldstein, Hammond_2020_Experimental, Albert_2021_Searching} (see, for a review \cite{Berthier_2019_Gardner}). For example, when studying `jamming' at zero -temperature, the question is posed as `on what side of the 1RSB-FRSB -transition are high energy (or low density) states reachable dynamically?' -In the present paper we give a concrete strategy to define unambiguously such -an issue: we consider the local energy minima at a given energy and study their -number and other properties: the solution involves a replica-symmetry breaking -scheme that is well-defined, and corresponds directly to the topological -characteristics of those minima. +temperature, the question is posed as `on what side of the 1RSB--FRSB +transition are high energy (or low density) states reachable dynamically?' One +approach to answering such questions makes use of `state following,' +which tracks metastable thermodynamic configurations to their zero temperature +limit \cite{Rainone_2015_Following, Biroli_2016_Breakdown, +Rainone_2016_Following, Biroli_2018_Liu-Nagel, Urbani_2017_Shear}. In the +present paper we give a purely geometric appoarch: we consider the local energy +minima at a given energy and study their number and other properties: the +solution involves a replica-symmetry breaking scheme that is well-defined, and +corresponds directly to the topological characteristics of those minima. Perhaps the most interesting application of this computation is in the context |