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diff --git a/response.txt b/response.txt deleted file mode 100644 index 1709e15..0000000 --- a/response.txt +++ /dev/null @@ -1,209 +0,0 @@ -\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: - -{\color{red} -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?) \cite{Ros_2019_Complexity, Ros_2021_Dynamical}, or the fate of long-time dynamics -(which end in what kind of target states?). - -} - -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 and PRX -- is rejected -because it demands of the readers a slightly longer attention span. - - - - -\begin{enumerate} - \item PRL has been publishing articles on precisely this problem in the - last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological} - \item These 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. -\end{enumerate} - - - -Below, we respond to the referees' comments. - -{\it Report of Referee A -- LY17256/Kent-Dobias - 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. - - 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. - - 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.} - - - -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 *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 -{\bf 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}. -%We disagree with the -%referee's implicit assertion that only clean resolutions, and not the -%compelling deepening of problems, are worthy of a broad audience. - -Report of Referee B -- LY17256/Kent-Dobias -{\it 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. - - } - -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: - -{\color{blue} - 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 \cite{Crisanti_1995_Thouless-Anderson-Palmer} (TAP) free energy, instead of the energy. We do not expect new features or technical -complications arise. - -} - - -%For a system where the quenched and annealed -%complexities differ, there has not been a correct calculation of the -%quenched complexity at finite temperature. (and, besides our work, -%only once or twice at zero temperature, e.g., PRX 9, 011003 (2019).) -%Rejecting a paper based on a severe misconception of its contents or -%of the state of the field is not appropriate. - -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 - - - Open a new research area, or a new avenue within an established area. - - Solve, or make essential steps towards solving, a critical problem. - - Introduce techniques or methods with significant impact. - - Be of unusual intrinsic interest to PRL's broad audience. - -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} |