Update on Overleaf.

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}