Worked on addressing the fitting questions from the first referee.

1 files changed, 35 insertions, 2 deletions

diff --git a/referee_comments.txt b/referee_comments.txt
index fd68ecc..d4740ff 100644
--- a/referee_comments.txt
+++ b/referee_comments.txt
@@ -23,17 +23,50 @@ form ε²η². In a new appendix, we have worked through the mean field modulus
 implied with this new interaction and a fit is now shown in Fig. 2 as a thin
 black line.
 
+An inset with a zoom on the critical region has been added to the figure.
+
 > Is it not clear how discriminatory is the agreement above TN in 2a, 2b 
 > and 2c. Are calculation results robust over a wide range of fitting 
 > parameters, or does the agreement result from a fine-tuning? (e.g., 
 > the presence of a maximum at 120 K in 2b). 
 
-[Not exactly sure what this means.] [I don't know either... let's think]
+In order to check the agreement in our fit, we preformed the fit with a moving
+temperature window that cuts off at T_max. Our fit's parameters are x_i for i =
+1, …, 5 for C₀ = x₁ - x₂ (T / K), x₃ = a/b², x₄ = b²/Dq⁴, and x₅ = b √(-g/u).
+The variation of these parameters as a function of T_max are shown in
+referee_response_cutoff_parameters.pdf. The parameter x₁ is fairly stable at
+all temperature cutoffs, while the rest vary by at most 20–60% of their 275K
+value down to cutoffs of ~90K.
+
+More insight into the consistency of the fit comes from examining the linear
+combinations of parameters that form eigenvectors of the fit covariance matrix,
+since these have uncorrelated uncertainties. For the fit including all
+temperatures (up to 275K), these are (in order of fit uncertainty):
+
+  y₁ = -0.00198126 x₁ + 2.16869 10⁻⁶ x₂ - 0.99998 x₃ - 0.00227756 x₄ - 0.00560291 x₅
+  y₂ = -0.0151198 x₁ + 0.0000415145 x₂ - 0.00552438 x₃ - 0.0205384 x₄ + 0.999659 x₅
+  y₃ = 0.635138 x₁ - 0.00196902 x₂ - 0.00315925 x₃ + 0.77197 x₄ + 0.0254495 x₅
+  y₄ = 0.772222 x₁ - 0.00663886 x₂ - 0.0000753204 x₃ - 0.635317 x₄ - 0.00137316 x₅
+  y₅ = 0.00637806 x₁ + 0.999976 x₂ - 4.32279 10⁻⁶ x₃ - 0.00269696 x₄ - 4.93718 10⁻⁷ x₅
+
+The variation of these parameter combinations as a function of T_max are shown
+in referee_response_cutoff_eigenvectors.pdf. The parameter y₁, which is
+principally x₃ = a/b², varies the most with the cutoff, at most around 60% of
+its value until ~90K. The parameter y₂, which is principally x₅ = b √(-g/u),
+varies at most around 15% of its value until ~90K. The other three parameters
+are stable at any cutoff, and are likewise mixed combinations of x₁, x₂, and
+x₄.
+
+Plots of the fits performed between 90 and 275 K are shown in
+referee_response_cutoff_curves.pdf.
 
 > Is it possible to say something about the c/a ratio, which displays a 
 > non-trivial T-dependence? 
 
-[Not sure what this means either. Is this asking about the ratio of lattice constants?] [yes]
+The c/a ratio is governed by the behavior of the A1g moduli, which exhibit no
+novel behavior in our theory. We therefore have nothing to say about it.
+
+[Add something to cite about why we shouldn't need to say something about this?]
 
 > At last, I understand that the model is meant to be purely 
 > phenomenological, but given the plethora of publications on URu2Si2