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| -rw-r--r-- | .gitignore | 11 | ||||
| -rw-r--r-- | bezout.bib | 10 | ||||
| -rw-r--r-- | bezout.tex | 42 |
3 files changed, 63 insertions, 0 deletions
diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..7c6e9d5 --- /dev/null +++ b/.gitignore @@ -0,0 +1,11 @@ +*.aux +*.bbl +*.blg +*.fdb_latexmk +*.fls +*.log +*Notes.bib +*.out +/*.pdf +*.dvi +*.synctex.gz diff --git a/bezout.bib b/bezout.bib new file mode 100644 index 0000000..0318f58 --- /dev/null +++ b/bezout.bib @@ -0,0 +1,10 @@ +@book{Bezout_1779_Theorie, + author = {Bézout, Etienne}, + title = {Théorie générale des équations algébriques}, + publisher = {L'imprimerie de Ph.-D. Pierres}, + year = {1779}, + url = {https://archive.org/details/thoriegnra00bz/}, + address = {rue S. Jacques, Paris} +} + + diff --git a/bezout.tex b/bezout.tex new file mode 100644 index 0000000..4abb8e2 --- /dev/null +++ b/bezout.tex @@ -0,0 +1,42 @@ +\documentclass[aps,prl,reprint,longbibliography,floatfix,fleqn]{revtex4-2} + +\usepackage[utf8]{inputenc} % why not type "Bézout" with unicode? +\usepackage[T1]{fontenc} % vector fonts plz +\usepackage[ + colorlinks=true, + urlcolor=purple, + citecolor=purple, + filecolor=purple, + linkcolor=purple +]{hyperref} % ref and cite links with pretty colors +\usepackage{amsmath, amssymb, graphicx, xcolor} % standard packages + +\begin{document} + +\title{Complex complex landscapes: saturating the Bézout bound} % change me + +\author{Jaron Kent-Dobias} +\author{Jorge Kurchan} + +\affiliation{Laboratoire de Physique de l'Ecole Normale Supérieure, Paris, France} + +\date\today + +\begin{abstract} + The complexity of the complex $p$-spin model saturates the Bézout bound \cite{Bezout_1779_Theorie}. +\end{abstract} + +\maketitle + +\begin{equation} \label{eq:hamiltonian} + H = \frac1{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p} +\end{equation} +where the $z$ are constrained by $z\cdot z=N$ and $J$ is a symmetric +tensor whose elements are complex normal with $\langle|J|^2\rangle=p!/2N^{p-1}$ +and $\langle J^2\rangle=\kappa\langle|J|^2\rangle$ for complex parameter +$|\kappa|<1$. + +\bibliographystyle{apsrev4-2} +\bibliography{bezout} + +\end{document} |