diff options
| -rw-r--r-- | bezout.bib | 25 | ||||
| -rw-r--r-- | bezout.tex | 4 |
2 files changed, 17 insertions, 12 deletions
@@ -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}, @@ -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. |