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diff --git a/response.tex b/response.tex new file mode 100644 index 0000000..4addddf --- /dev/null +++ b/response.tex @@ -0,0 +1,197 @@ +\documentclass[a4paper]{letter} + +\usepackage[utf8]{inputenc} % why not type "Bézout" with unicode? +\usepackage[T1]{fontenc} % vector fonts plz +\usepackage{newtxtext,newtxmath} % Times for PR +\usepackage[ + colorlinks=true, + urlcolor=purple, + linkcolor=black, + citecolor=black, + filecolor=black, +]{hyperref} % ref and cite links with pretty colors +\usepackage{xcolor} +\usepackage[style=phys]{biblatex} + +\renewcommand{\thefootnote}{\fnsymbol{footnote}} + +\addbibresource{frsb_kac-rice.bib} + +\signature{ + \vspace{-6\medskipamount} + \smallskip + Jaron Kent-Dobias \& Jorge Kurchan +} + +\address{ + Laboratoire de Physique\\ + Ecole Normale Sup\'erieure\\ + 24 rue Lhomond\\ + 75005 Paris +} + +\begin{document} +\begin{letter}{ + Agnese I.~Curatolo, Ph.D.\\ + Physical Review Letters\\ + 1 Research Road\\ + Ridge, NY 11961 +} + +\opening{Dear Dr.~Curatolo,} + +Enclosed please find a revised manuscript. +Neither referee criticized the scientific content of our paper, +nor substantively addressed its presentation. We have followed their comments +in the direction of highlighting the importance of having a full solution. In particular +we have emphasized that going to the full replica treatment uncovers a phase-space structure that needs to be taken into account, and that is absent in the annealed treatment. + + +We have thus added the paragraph: + +\begin{quote} +Having a full, exact (`quenched') solution of the generic problem is not +primarily a matter of {\em accuracy}. +Very basic structural questions are omitted in the approximate `annealed' solution. What is lost is the nature, at any given +energy (or free energy) level, of the stationary points in a generic energy function: at low energies are they basically all minima, with an exponentially small number of saddles, or +-- as we show here -- do they consist of a mixture of saddles whose index -- the number of unstable directions -- is a smoothly distributed number? +These questions need to be answered for the understanding of the relevance of more complex objects such as +barrier crossing (which barriers?) \footfullcite{Ros_2019_Complexity, Ros_2021_Dynamical}, or the fate of long-time dynamics +(which end in what kind of target states?). +\end{quote} + +Both referees find that our paper is clearly written but technical, and +that its topic of ``the different RSB schemes'' are not suitable for a +broad audience. This is surprising to the authors, since a quick +search on Google Scholar reveals several recent PRLs with heavy use of +RSB schemes. + +We would also like to submit to the referees that it is somewhat incongruous +that the solution to a problem that had remained open for 42 years -- during +which it was always present in articles in PRL +\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, +Fyodorov_2012_Critical, Wainrib_2013_Topological, Dennis_2020_Jamming}-- is +rejected because it demands of the readers a slightly longer attention span. +These previous works were often limited by the fact that general landscapes +(for which an annealed solution is not exact) were inaccessible. It is perhaps +true that the final solution of an open problem may often be more technical +than the previous ones. + + +Below, we respond to the referees' comments. + +\begin{quote} + \begin{center} + Report of Referee A -- LY17256/Kent-Dobias + \end{center} + \it + The authors consider spin glass models with mixed p-spin interactions + on the N-Sphere and calculate the number of stationary points, the + logarithm of which yields the complexity. The disorder average of this + logarithm is computed with the replica trick, and for different model + variants different replica symmetry breaking (RSB) solutions are + obtained. A new feature of the solutions, in contrast to previous + replica symmetric calculations, is that RSB must occur in parts of the + energy-stability phase diagram. + + \hspace{2em}The paper is clearly written although the content is rather technical + and probably only accessible to experts in mean field spin glass + models and the different RSB schemes developed in this field. In + connection with the well-studied p=3 spin glass model it is briefly + mentioned that the complexity and its transitions as a function of + energy and/or stability is relevant for the equilibrium and the + dynamical behavior of this model – but such a connection has not been + made here. + + \hspace{2em}Therefore, I feel that the results presented here are only interesting + for group of experts and I do not assess the finding that the + complexity of mixed p-spin glass models shows RSB as a major + breakthrough in the field. Therefore, the manuscript is not suitable + for publication in Phys.\ Rev.\ Lett., and the publication of the + accompanying longer paper, submitted to PRE, is sufficient to + disseminate the results summarized in this manuscript. +\end{quote} + + +Referee A correctly points out that one new feature of the solutions +outlined in our manuscript is that RSB must occur in parts of the +phase diagram for these models. However, they neglect another feature: +that they are the solutions of the \textit{quenched} complexity, which has +not been correctly calculated until now. We agree with the referee +that ``the complexity of the mixed p-spin glass models'' is not a major +breakthrough in and of itself, we just +chose to demonstrate the problem in simplest toy model. But believe that the technique for +computing the quenched complexity is a major breakthrough +\textit{because it brings in the features of organization of saddles of all +kinds that are invisible in the annealed scheme}. + + +Referee A states that a connection between the complexity and the +equilibrium and dynamical behavior is not made in our paper. Until +recently, this connection was taken for granted, and the demonstration +that the standard correspondence does not hold in the mixed p-spin +spherical models was exciting enough news to be published in PRX 10, +031045 (2020). It is true that our work doesn't solve the problem that +paper opened, but it does deepen it by showing definitively that the +use of RSB and the quenched complexity are not sufficient to +reestablish a landscape–dynamics connection. +{\bf One can hardly expect that the structure of saddles at a given energy may be connected +with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}. + +\begin{quote} + \begin{center} + Report of Referee B -- LY17256/Kent-Dobias + \end{center} + \textit{The paper presents a computation of the complexity in spherical + spin-glass models. Neither the techniques nor the results are + sufficiently new and relevant to justify publication on PRL. This is + not surprising given that the topic has been studied extensively in + the last thirty years and more, the only novelty with respect to + previous work is that the results are obtained at zero temperature but + this is definitively not enough. Essential open problems in the field + involves dynamics and activated processes and some results have + appeared recently, instead the analysis of the static landscape, to + which the present paper is a variation, failed to deliver answers to + these questions up to now. + } +\end{quote} + +Concerning the statement of Referee B that ``the only novelty +with respect to previous work is that the results are obtained at zero +temperature,'' we do not know what to make of the referee's statement. +The novelty of the paper is most definitely +not the fact of treating a zero temperature case. +We have added the following phrase, that should clarify the situation: + + For simplicity we have concentrated here on the energy, rather +than {\em free-energy} landscape, although the latter is sometimes +more appropriate. From the technical point of view, this makes no fundamental difference, it suffices +to apply the same computation to the Thouless-Andreson-Palmer (TAP) free energy, \footfullcite{Crisanti_1995_Thouless-Anderson-Palmer} instead of the energy. We do not expect new features or technical +complications arise. + +We agree with Referee B's assessment of ``essential open problems in +the field,'' and agree that our work does not deliver answers. However, +delivering answers for all essential open problems is not the acceptance +criterion of PRL. These are + +\begin{itemize} + \item Open a new research area, or a new avenue within an established area. + \item Solve, or make essential steps towards solving, a critical problem. + \item Introduce techniques or methods with significant impact. + \item Be of unusual intrinsic interest to PRL's broad audience. +\end{itemize} + +We believe our manuscript makes essential steps toward solving the +critical problem of connecting analysis of the static landscape to +dynamics. We believe that its essential step is through the +introduction of a new technique, calculation of the quenched +complexity, which we believe will have significant impact as it is +applied to more complicated models. + +\closing{Sincerely,} + +\vspace{1em} + +\end{letter} + +\end{document} |