Standardized references.

2 files changed, 92 insertions, 73 deletions

diff --git a/frsb_kac-rice.bib b/frsb_kac-rice.bib
index 48b4e3e..52f12f5 100644
--- a/frsb_kac-rice.bib
+++ b/frsb_kac-rice.bib
@@ -54,6 +54,20 @@
  doi = {10.1002/cpa.21875}
 }
 
+@article{Bray_1980_Metastable,
+ author = {Bray, A J and Moore, M A},
+ title = {Metastable states in spin glasses},
+ journal = {Journal of Physics C: Solid State Physics},
+ publisher = {IOP Publishing},
+ year = {1980},
+ month = {7},
+ number = {19},
+ volume = {13},
+ pages = {L469--L476},
+ url = {https://doi.org/10.1088%2F0022-3719%2F13%2F19%2F002},
+ doi = {10.1088/0022-3719/13/19/002}
+}
+
 @article{Bray_2007_Statistics,
  author = {Bray, Alan J. and Dean, David S.},
  title = {Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces},
@@ -96,6 +110,20 @@
  doi = {10.1007/bf01312184}
 }
 
+@article{Crisanti_1995_Thouless-Anderson-Palmer,
+ author = {Crisanti, A. and Sommers, H.-J.},
+ title = {Thouless-Anderson-Palmer Approach to the Spherical p-Spin Spin Glass Model},
+ journal = {Journal de Physique I},
+ publisher = {EDP Sciences},
+ year = {1995},
+ month = {7},
+ number = {7},
+ volume = {5},
+ pages = {805--813},
+ url = {https://doi.org/10.1051%2Fjp1%3A1995164},
+ doi = {10.1051/jp1:1995164}
+}
+
 @article{Crisanti_2004_Spherical,
  author = {Crisanti, A. and Leuzzi, L.},
  title = {Spherical $2+p$ Spin-Glass Model: An Exactly Solvable Model for Glass to Spin-Glass Transition},
@@ -152,6 +180,62 @@
  type = {Theses}
 }
 
+@article{Fyodorov_2007_Replica,
+ author = {Fyodorov, Yan V. and Williams, Ian},
+ title = {Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity},
+ journal = {Journal of Statistical Physics},
+ publisher = {Springer Science and Business Media LLC},
+ year = {2007},
+ month = {9},
+ number = {5-6},
+ volume = {129},
+ pages = {1081--1116},
+ url = {https://doi.org/10.1007%2Fs10955-007-9386-x},
+ doi = {10.1007/s10955-007-9386-x}
+}
+
+@article{Mezard_1992_Manifolds,
+ author = {Mézard, M. and Parisi, G.},
+ title = {Manifolds in random media: two extreme cases},
+ journal = {Journal de Physique I},
+ publisher = {EDP Sciences},
+ year = {1992},
+ month = {12},
+ number = {12},
+ volume = {2},
+ pages = {2231--2242},
+ url = {https://doi.org/10.1051%2Fjp1%3A1992278},
+ doi = {10.1051/jp1:1992278}
+}
+
+@article{Parisi_1979_Infinite,
+ author = {Parisi, G.},
+ title = {Infinite Number of Order Parameters for Spin-Glasses},
+ journal = {Physical Review Letters},
+ publisher = {American Physical Society (APS)},
+ year = {1979},
+ month = {12},
+ number = {23},
+ volume = {43},
+ pages = {1754--1756},
+ url = {https://doi.org/10.1103%2Fphysrevlett.43.1754},
+ doi = {10.1103/physrevlett.43.1754}
+}
+
+@article{Rieger_1992_The,
+ author = {Rieger, H.},
+ title = {The number of solutions of the {Thouless}-{Anderson}-{Palmer} equations for {$p$}-spin-interaction spin glasses},
+ journal = {Physical Review B},
+ publisher = {American Physical Society (APS)},
+ year = {1992},
+ month = {12},
+ number = {22},
+ volume = {46},
+ pages = {14655--14661},
+ url = {https://doi.org/10.1103%2Fphysrevb.46.14655},
+ doi = {10.1103/physrevb.46.14655}
+}
+
 @article{Ros_2019_Complex,
  author = {Ros, Valentina and Ben Arous, Gerard and Biroli, Giulio and Cammarota, Chiara},
  title = {Complex Energy Landscapes in Spiked-Tensor and Simple Glassy Models: Ruggedness, Arrangements of Local Minima, and Phase Transitions},
@@ -165,70 +249,5 @@
  url = {https://doi.org/10.1103%2Fphysrevx.9.011003},
  doi = {10.1103/physrevx.9.011003}
 }
-@article{bray1980metastable,
-  title={Metastable states in spin glasses},
-  author={Bray, Alan J and Moore, Michael A},
-  journal={Journal of Physics C: Solid State Physics},
-  volume={13},
-  number={19},
-  pages={L469},
-  year={1980},
-  publisher={IOP Publishing}
-}
-
-@article{parisi1979infinite,
-  title={Infinite number of order parameters for spin-glasses},
-  author={Parisi, Giorgio},
-  journal={Physical Review Letters},
-  volume={43},
-  number={23},
-  pages={1754},
-  year={1979},
-  publisher={APS}
-}
-
-@article{rieger1992number,
-  title={The number of solutions of the Thouless-Anderson-Palmer equations for p-spin-interaction spin glasses},
-  author={Rieger, Heiko},
-  journal={Physical Review B},
-  volume={46},
-  number={22},
-  pages={14655},
-  year={1992},
-  publisher={APS}
-}
-@article{fyodorov2007replica,
-  title={Replica symmetry breaking condition exposed by random matrix calculation of landscape complexity},
-  author={Fyodorov, Yan V and Williams, Ian},
-  journal={Journal of Statistical Physics},
-  volume={129},
-  number={5},
-  pages={1081--1116},
-  year={2007},
-  publisher={Springer}
-}
-
-
-
-
-@article{mezard1992manifolds,
-  title={Manifolds in random media: two extreme cases},
-  author={M{\'e}zard, Marc and Parisi, Giorgio},
-  journal={Journal de Physique I},
-  volume={2},
-  number={12},
-  pages={2231--2242},
-  year={1992},
-  publisher={EDP Sciences}
-}
-
-@article{crisanti1995thouless,
-  title={Thouless-Anderson-Palmer approach to the spherical p-spin spin glass model},
-  author={Crisanti, Andrea and Sommers, H-J},
-  journal={Journal de Physique I},
-  volume={5},
-  number={7},
-  pages={805--813},
-  year={1995},
-  publisher={EDP Sciences}
-}
+
+
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 3b06750..1b16410 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -15,17 +15,17 @@
 
 The computation of the number of metastable states of mean field spin glasses
 goes back to the beginning of the field. Over forty years ago,
- Bray and Moore \cite{bray1980metastable} attempted the first calculation for 
+Bray and Moore \cite{Bray_1980_Metastable} attempted the first calculation for 
  the Sherrington-Kirkpatrick model, a paper remarkable for being the first practical application of a replica symmetry breaking scheme. As became clear when the actual
- ground-state of the model was computed by Parisi \cite{parisi1979infinite}, the Bray-Moore result
+ ground-state of the model was computed by Parisi \cite{Parisi_1979_Infinite}, the Bray-Moore result
  was not exact, and
 in fact  the problem has been open 
 ever since.
 Indeed, to this date the program of computing the number of saddles of a mean-field 
 glass has been only  carried out for a small subset of models.
-These include most notably the p-spin model ($p>2$) \cite{rieger1992number,crisanti1995thouless}. 
+These include most notably the p-spin model ($p>2$) \cite{Rieger_1992_The, Crisanti_1995_Thouless-Anderson-Palmer}. 
 The problem of studying the critical points of these landscapes
-has evolved into an active field in probability theory \cite{Auffinger_2012_Random,Auffinger_2013_Complexity,BenArous_2019_Geometry}
+has evolved into an active field in probability theory \cite{Auffinger_2012_Random, Auffinger_2013_Complexity, BenArous_2019_Geometry}
 
 In this paper we present what we believe is the general ansatz for the 
 computation of saddles of generic mean-field models,  including the Sherrington-Kirkpatrick model. It incorporates  the Parisi solution as the limit of lowest states, as it should.
@@ -34,7 +34,7 @@ computation of saddles of generic mean-field models,  including the Sherrington-
 \section{The model}
 
 Here we consider, for definiteness, the  mixed $p$-spin model, itself a particular case 
-of the `Toy Model' of M\'ezard and Parisi \cite{mezard1992manifolds}
+of the `Toy Model' of M\'ezard and Parisi \cite{Mezard_1992_Manifolds}
 \begin{equation}
   H(s)=\sum_p\frac{a_p^{1/2}}{p!}\sum_{i_1\cdots i_p}J_{i_1\cdots i_p}s_{i_1}\cdots s_{i_p}
 \end{equation}
@@ -327,7 +327,7 @@ This will turn out to be important when we discriminate between counting all sol
 As noted by Bray and Dean  \cite{Bray_2007_Statistics}, gradient and Hessian are independent
 for a Gaussian distribution, and
 the average over disorder breaks into a product of two independent averages, one for the gradient factor and one for the determinant. The integration of all variables, including the disorder in the last factor, may be restricted to the domain such that the matrix $\partial\partial H(s_a)-\mu I$ has  a specified number of negative eigenvalues (the index {\cal{I}} of the saddle), 
-(see Fyodorov \cite{fyodorov2007replica} for a detailed discussion) }
+(see Fyodorov \cite{Fyodorov_2007_Replica} for a detailed discussion) }
 
 \begin{equation}
   \begin{aligned}