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authorJaron Kent-Dobias <jaron@kent-dobias.com>2023-01-23 12:00:35 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2023-01-23 12:00:35 +0100
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@@ -87,33 +87,35 @@ because it demands of the readers a slightly longer attention span.
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.}
-
+Report of Referee A -- LY17256/Kent-Dobias
+\begin{quote}
+ \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
@@ -145,19 +147,20 @@ with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}.
%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.
-
- }
+\begin{quote}
+ \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
@@ -188,10 +191,12 @@ 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.
+\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