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| -rw-r--r-- | frsb_kac-rice.bib | 20 | ||||
| -rw-r--r-- | frsb_kac-rice.tex | 19 |
2 files changed, 32 insertions, 7 deletions
diff --git a/frsb_kac-rice.bib b/frsb_kac-rice.bib index 27eccde..24ae002 100644 --- a/frsb_kac-rice.bib +++ b/frsb_kac-rice.bib @@ -165,5 +165,25 @@ url = {https://doi.org/10.1103%2Fphysrevx.9.011003}, doi = {10.1103/physrevx.9.011003} } +@article{bray1980metastable, + title={Metastable states in spin glasses}, + author={Bray, Alan J and Moore, Michael A}, + journal={Journal of Physics C: Solid State Physics}, + volume={13}, + number={19}, + pages={L469}, + year={1980}, + publisher={IOP Publishing} +} +@article{parisi1979infinite, + title={Infinite number of order parameters for spin-glasses}, + author={Parisi, Giorgio}, + journal={Physical Review Letters}, + volume={43}, + number={23}, + pages={1754}, + year={1979}, + publisher={APS} +} diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index df30c38..357f4e6 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -13,14 +13,19 @@ \end{abstract} \section{Introduction} - -Although the Bray-Moore computation for the SK model was the first application of -some replica symmetry breaking scheme, it turned out that the problem has been open +The computation of the number of metastable states of mean field spin glasses +goes back to the beginning of the field. Over forty years ago, + Bray and Moore \cite{bray1980metastable} attempted the first calculation for + the Sherrington-Kirkpatrick model, a paper remarkable for being the first practical application of a replica symmetry breaking scheme. As became clear when the actual + ground-state of the model was computed by Parisi \cite{parisi1979infinite}, the Bray-Moore result + was not exact, and +in fact the problem has been open ever since. - -to this date the program has been only complete for a subset of models - -here we present what we believe is the general scheme +Indeed, to this date the program of computing the number of saddles of a mean-field +glass has been only carried out for a small subset of models. +These include most notable the p-spin model ($p>2$) \cite{rie +In this paper we present what we believe is the general ansatz for the solution. +It includes the Parisi solution as the limit of lowest states, as it should. \subsection{What to expect?} |