From 034be30931cea7a5870e33b925de49e19dd6d92a Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 9 Dec 2020 17:41:30 +0100 Subject: Updated reference. --- bezout.bib | 25 +++++++++++++++---------- bezout.tex | 4 ++-- 2 files changed, 17 insertions(+), 12 deletions(-) diff --git a/bezout.bib b/bezout.bib index 51df35d..c82da78 100644 --- a/bezout.bib +++ b/bezout.bib @@ -11,16 +11,7 @@ url = {https://doi.org/10.1007%2Fjhep12%282016%29071}, doi = {10.1007/jhep12(2016)071} } -@article{bogomolny1992distribution, - title={Distribution of roots of random polynomials}, - author={Bogomolny, Eugene and Bohigas, Oriol and Leboeuf, Patricio}, - journal={Physical Review Letters}, - volume={68}, - number={18}, - pages={2726}, - year={1992}, - publisher={APS} -} + @article{Antenucci_2015_Complex, author = {Antenucci, F. and Crisanti, A. and Leuzzi, L.}, title = {Complex spherical {$2+4$} spin glass: A model for nonlinear optics in random media}, @@ -72,6 +63,20 @@ address = {rue S. Jacques, Paris} } +@article{Bogomolny_1992_Distribution, + author = {Bogomolny, E. and Bohigas, O. and Leboeuf, P.}, + title = {Distribution of roots of random polynomials}, + journal = {Physical Review Letters}, + publisher = {American Physical Society (APS)}, + year = {1992}, + month = {5}, + number = {18}, + volume = {68}, + pages = {2726--2729}, + url = {https://doi.org/10.1103%2Fphysrevlett.68.2726}, + doi = {10.1103/physrevlett.68.2726} +} + @article{Bray_1980_Metastable, author = {Bray, A J and Moore, M A}, title = {Metastable states in spin glasses}, diff --git a/bezout.tex b/bezout.tex index 21d8146..4202e9b 100644 --- a/bezout.tex +++ b/bezout.tex @@ -69,7 +69,7 @@ complex variables, and the roots are simple all the way (we shall confirm this), variables minima of functions appear and disappear, and this procedure is not possible. The same idea may be implemented by performing diffusion in the $J$'s, and following the roots, in complete analogy with Dyson's stochastic dynamics. -This study also provides a complement to the work on the distribution of zeroes of random polynomials \cite{bogomolny1992distribution}. +This study also provides a complement to the work on the distribution of zeroes of random polynomials \cite{Bogomolny_1992_Distribution}. Let us go back to our model. @@ -319,7 +319,7 @@ The number of critical points contained within is =(p-1)^{N/2}, \end{equation} the square root of \eqref{eq:bezout} and precisely the number of critical -points of the real pure spherical $p$-spin model. (note the role of conjugation symmetry, already underlined in Ref\cite{bogomolny1992distribution}). In fact, the full +points of the real pure spherical $p$-spin model. (note the role of conjugation symmetry, already underlined in Ref\cite{Bogomolny_1992_Distribution}). In fact, the full $\epsilon$-dependence of the real pure spherical $p$-spin is recovered by this limit as $\epsilon$ is varied. -- cgit v1.2.3-54-g00ecf