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# Report #1
-Please find below a short list of comments/ typos:
-
--Some of the results derived for the spherical spin-glass stem from the limit mentioned above. It is clear that this limit may be relevant as some important energy scales are recovered that way. Note however that starting from a regime α=M/N=O(1)
-and taking the limit α→0 should in fact match with the limit M→∞ of the regime M=O(1). Thus there is no guarantee that it should provide relevant information on the case M=1. A direct study of the level set of the spherical spin-glass model as done in Appendix D should allow to confirm this prediction. It was not entirely clear from the manuscript whether this analysis indeed does confirm the relevance of Esh
-
-.
-
--As mentioned by the author, the numerical data does not allow to judge the relevance of the energy scale Esh
-
-and this direction deserves further investigation
-Recommendation
-
-Publish (meets expectations and criteria for this Journal)
-
- validity: high
- significance: high
- originality: high
- clarity: high
- formatting: excellent
- grammar: perfect
-
* We fixed this typo.
* The question of limits is a shrewd one, but ultimately the result is the same no matter how the calculation is done. Working directly at *M* = 1, the steps in the appendices are followed up to equation (28). With *M* = 1 and *V*₀² = *N**E*, the second term in the exponential remains of order *N* but the second is of order 1 and becomes another contribution to the prefactor. Comparing the resulting expression with (41) in the limit of α to zero with *V*₀² = *E*²/α, the two approaches result in the same effective action. In fact, an earlier version of this manuscript included two derivations, but the one for *M* of order 1 was deemed redundant in light of this. A note about this point has been added to the amended manuscript.
* We agree, and further emphasized this in the amended manuscript.