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author | kurchan.jorge <kurchan.jorge@gmail.com> | 2020-12-09 12:31:36 +0000 |
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committer | overleaf <overleaf@localhost> | 2020-12-09 12:32:38 +0000 |
commit | 2d8dabac48abecb6a96376161c4f70846f27de4d (patch) | |
tree | 70f8536ad82835b46bf07cab92763b7818191447 | |
parent | 101a3dd52c972252c3c606a51c33f87693d96c50 (diff) | |
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Update on Overleaf.
-rw-r--r-- | bezout.bib | 10 | ||||
-rw-r--r-- | bezout.tex | 4 |
2 files changed, 12 insertions, 2 deletions
@@ -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}, @@ -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, |