summaryrefslogtreecommitdiff
diff options
context:
space:
mode:
authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-09 13:32:39 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-09 13:32:39 +0100
commit32e931a81593e53ca6c81d272b7adbe7158de013 (patch)
treedd3de9a9748144804f813d42d518d4c26b9ee680
parent642d314550029619215cb38cbebcecbbf2f98850 (diff)
parent2d8dabac48abecb6a96376161c4f70846f27de4d (diff)
downloadPRR_3_023064-32e931a81593e53ca6c81d272b7adbe7158de013.tar.gz
PRR_3_023064-32e931a81593e53ca6c81d272b7adbe7158de013.tar.bz2
PRR_3_023064-32e931a81593e53ca6c81d272b7adbe7158de013.zip
Merge branch 'master' of https://git.overleaf.com/5fcce4736e7f601ffb7e1484
-rw-r--r--bezout.bib10
-rw-r--r--bezout.tex4
2 files changed, 12 insertions, 2 deletions
diff --git a/bezout.bib b/bezout.bib
index 37e8f33..a23955b 100644
--- a/bezout.bib
+++ b/bezout.bib
@@ -194,6 +194,16 @@
year={1992},
publisher={Springer}
}
+@article{castellani2005spin,
+ title={Spin-glass theory for pedestrians},
+ author={Castellani, Tommaso and Cavagna, Andrea},
+ journal={Journal of Statistical Mechanics: Theory and Experiment},
+ volume={2005},
+ number={05},
+ pages={P05012},
+ year={2005},
+ publisher={IOP Publishing}
+}
@article{cugliandolo1993analytical,
title={Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model},
diff --git a/bezout.tex b/bezout.tex
index 753b65b..702f1ae 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -39,14 +39,14 @@ different topological properties.
Spin-glasses have long been considered the paradigm of `complex landscapes' of many variables, a subject that
includes Neural Networks and optimization problems, most notably Constraint Satisfaction ones.
-The most tractable family of these are the mean-field spherical p-spin models \cite{crisanti1992sphericalp}
+The most tractable family of these are the mean-field spherical p-spin models \cite{crisanti1992sphericalp} (for a review see \cite{castellani2005spin})
defined by the energy:
\begin{equation} \label{eq:bare.hamiltonian}
H_0 = \sum_p \frac{c_p}{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p},
\end{equation}
where the $J_{i_1\cdots i_p}$ are real Gaussian variables and the $z_i$ are real and constrained
to a sphere $\sum_i z_i^2=N$. If there is a single term of a given $p$, this is known as the `pure $p$-spin' model, the case we shall study here.
-Also in the algebra \cite{cartwright2013number} and probability literature \cite{auffinger2013complexity,auffinger2013random}
+Also in the Algebra \cite{cartwright2013number} and Probability literature \cite{auffinger2013complexity,auffinger2013random}.
This problem has been attacked from several angles: the replica trick to
compute the Boltzmann--Gibbs distribution\cite{crisanti1992sphericalp}, a Kac--Rice \cite{Kac_1943_On,