Edited the referee response.

1 files changed, 20 insertions, 7 deletions

diff --git a/referee_response.tex b/referee_response.tex
index b33d3b1..0f2ce95 100644
--- a/referee_response.tex
+++ b/referee_response.tex
@@ -13,7 +13,22 @@
 First, we would like to apologize for the large delay in resubmission. As is
 evident, the manuscript has undergone a significant transformation as a result
 of the reviews we received. We would like to thank the reviewers for their
-helpful notes on the original manuscript.
+helpful notes on the original manuscript. The first reviewer was supportive and
+asked instructive questions. The second reviewer, though critical, led us to
+some great insights.
+
+The manuscript now focuses on the approximation of the 2D Ising universal
+scaling function by a smooth functional form. Though the singularity discussed
+in the original manuscript still plays an important role, our approximation now
+encompasses the whole parameter space of the relevant scaling fields. We
+compare this form to the values of the universal scaling function and its
+derivatives previously measured in the literature, and find exponential
+convergence with the amount of data fit.
+
+We believe that the substantial changes to our manuscript merit its
+reconsideration for publication. Though the new manuscript is so different from
+the old one as to likely deserve a new reviewing cycle, we respond to the
+original reviews here, to make clear how the revised manuscript addresses them.
 
 \begin{verbatim}
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@@ -169,9 +184,7 @@ where scattering in the Ising field theory is extensively discussed.
 \end{verbatim}
 
 We thank the referee for their helpful references, and we have cited the first
-two. The second one was especially relevant to our study. We don't see the
-relevance of the scattering to the scaling functions we study here, but perhaps
-future work may examine it as well.
+two. The second one was especially relevant to our study.
 
 \begin{verbatim}
 2. Several references are clearly not understood. The authors state
@@ -202,11 +215,11 @@ predict similar singularities..." have no place in a scientific paper.
 
 We believe that our transformed technique and manuscript can substantiate this
 claim, in a specific sense. Though the free energy computed point by point in
-our references by Mangazeev et al. and Fonseca et al. are more accurate, they
+our references by Mangazeev et al.\ and Fonseca et al.\ are more accurate, they
 are not functional forms: they are tables of data. We now show in the
-manuscript that our functional form exponentially approaches the numeric values
+manuscript that our functional form approaches the numeric values
 of the scaling function and its derivatives measured in the aforementioned
-works.
+works exponentially with iterative fitting.
 
 \begin{verbatim}
 4. The statement "Our forms both exhibit incorrect low-order