Changes based on Urbani's feedback.

2 files changed, 80 insertions, 7 deletions

diff --git a/frsb_kac-rice.bib b/frsb_kac-rice.bib
index 3c4b031..9a4e17a 100644
--- a/frsb_kac-rice.bib
+++ b/frsb_kac-rice.bib
@@ -124,6 +124,34 @@
  doi = {10.1063/1.5097175}
 }
 
+@article{Biroli_2016_Breakdown,
+ author = {Biroli, Giulio and Urbani, Pierfrancesco},
+ title = {Breakdown of elasticity in amorphous solids},
+ journal = {Nature Physics},
+ publisher = {Springer Science and Business Media LLC},
+ year = {2016},
+ month = {8},
+ number = {12},
+ volume = {12},
+ pages = {1130--1133},
+ url = {https://doi.org/10.1038%2Fnphys3845},
+ doi = {10.1038/nphys3845}
+}
+
+@article{Biroli_2018_Liu-Nagel,
+ author = {Biroli, Giulio and Urbani, Pierfrancesco},
+ title = {{Liu}-{Nagel} phase diagrams in infinite dimension},
+ journal = {SciPost Physics},
+ publisher = {Stichting SciPost},
+ year = {2018},
+ month = {4},
+ number = {4},
+ volume = {4},
+ pages = {020},
+ url = {https://doi.org/10.21468%2Fscipostphys.4.4.020},
+ doi = {10.21468/scipostphys.4.4.020}
+}
+
 @article{Bray_1980_Metastable,
  author = {Bray, A J and Moore, M A},
  title = {Metastable states in spin glasses},
@@ -691,6 +719,34 @@ stochastic localization},
  doi = {10.1088/0305-4470/13/5/047}
 }
 
+@article{Rainone_2015_Following,
+ author = {Rainone, Corrado and Urbani, Pierfrancesco and Yoshino, Hajime and Zamponi, Francesco},
+ title = {Following the Evolution of Hard Sphere Glasses in Infinite Dimensions under External Perturbations: Compression and Shear Strain},
+ journal = {Physical Review Letters},
+ publisher = {American Physical Society (APS)},
+ year = {2015},
+ month = {1},
+ number = {1},
+ volume = {114},
+ pages = {015701},
+ url = {https://doi.org/10.1103%2Fphysrevlett.114.015701},
+ doi = {10.1103/physrevlett.114.015701}
+}
+
+@article{Rainone_2016_Following,
+ author = {Rainone, Corrado and Urbani, Pierfrancesco},
+ title = {Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution},
+ journal = {Journal of Statistical Mechanics: Theory and Experiment},
+ publisher = {IOP Publishing},
+ year = {2016},
+ month = {5},
+ number = {5},
+ volume = {2016},
+ pages = {053302},
+ url = {https://doi.org/10.1088%2F1742-5468%2F2016%2F05%2F053302},
+ doi = {10.1088/1742-5468/2016/05/053302}
+}
+
 @article{Rice_1939_The,
  author = {Rice, S. O.},
  title = {The Distribution of the Maxima of a Random Curve},
@@ -775,6 +831,20 @@ stochastic localization},
  doi = {10.1103/physrevlett.117.228001}
 }
 
+@article{Urbani_2017_Shear,
+ author = {Urbani, Pierfrancesco and Zamponi, Francesco},
+ title = {Shear Yielding and Shear Jamming of Dense Hard Sphere Glasses},
+ journal = {Physical Review Letters},
+ publisher = {American Physical Society (APS)},
+ year = {2017},
+ month = {1},
+ number = {3},
+ volume = {118},
+ pages = {038001},
+ url = {https://doi.org/10.1103%2Fphysrevlett.118.038001},
+ doi = {10.1103/physrevlett.118.038001}
+}
+
 @article{Xiao_2022_Probing,
  author = {Xiao, Hongyi and Liu, Andrea J. and Durian, Douglas J.},
  title = {Probing {Gardner} Physics in an Active Quasithermal Pressure-Controlled Granular System of Noncircular Particles},
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