Update on Overleaf.

1 files changed, 13 insertions, 37 deletions

diff --git a/referee_comments.txt b/referee_comments.txt
index d4740ff..c246631 100644
--- a/referee_comments.txt
+++ b/referee_comments.txt
@@ -17,11 +17,7 @@
 > look plausible as the disagreement does not appear to develop slowly 
 > as T decreases, but appears immediately below TN, where eta is small. 
 
-The disagreement between the theory at low temperature is largely resolved by
-the addition of an additional interaction in the mean-field free energy of the
-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.
+The disagreement between the theory at low temperature is largely resolved by the addition of an additional interaction in the mean-field free energy of the 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.
 
@@ -30,18 +26,9 @@ An inset with a zoom on the critical region has been added to the figure.
 > parameters, or does the agreement result from a fine-tuning? (e.g., 
 > the presence of a maximum at 120 K in 2b). 
 
-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.
+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):
+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
@@ -49,13 +36,8 @@ temperatures (up to 275K), these are (in order of fit uncertainty):
   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.
+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.
@@ -63,10 +45,8 @@ referee_response_cutoff_curves.pdf.
 > Is it possible to say something about the c/a ratio, which displays a 
 > non-trivial T-dependence? 
 
-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.
+The behaviour of c/a is indeed interesting, but our model only considers the coupling to the two in-plane shear strains, since it is one of these that shows the anomalous behaviour. To talk about the c/a ratio we would have to introduce coupling between the order parameter and the A1g strains (\epsilon_xx + \epsilon_yy, and \epsilon_zz). Because the order parameter we consider breaks both translational and (locally) point-group symmetries, this coupling would be quadratic-in-order-parameter, linear-in-strain, and would thus be generic to any order parameter. Put more simply - our model has special coupling to a particular shear strain, whereas the c/a ratio is related to compresisonal strains, which couples to our order parameter in the same way as it does to any other (non-A_1g) order parameter. 
 
-[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 
@@ -103,7 +83,9 @@ This is a consistent with hexadecapolar order
 > within the mean-field treatment and does not provide a novel 
 > theoretical advance. 
 
-[hmmmm what can you say to this. i guess we can emphasize the part you did that IS new, at least we think it's new. Also, what's wrong with using existing, working tools for sovling problem?!?!!!!?!?!?! Does everyone have to come up with some black-hole-based-nonsense every time they solve a problem?]
+[Jaron will talk about what is new from his results. Below is Brad's more general statement]
+
+What our manuscript provides is a new way of interpreting a very clear experimental signature - that is, nearly perfect Curie-Weiss 1/(T-T_0) in (c11-c12)/2. We show that a staggered nematic order parameter explains this behaviour. We agree that coupling strains and order parameters is not new, but we do not believe that every scientific advance has to be accompanied by new mathematical machinery for its own sake. Mean-field-theory happens to work quite well here, and allows us to make clear symmetry-based statements. 
 
 > 
 > 2) One can generically expect several sources for softening elastic 
@@ -112,7 +94,7 @@ This is a consistent with hexadecapolar order
 > T_HO. Thus, the fitting is not regarded as the decisive evidence on 
 > the validity of the model. 
 
-[Not sure how to respond to this; Brad?] [yeah Curie-weiss is generic, that's true. ref 25 is also purely phenomenological (I'm guessing, haven't looked yet), we have testable predictions and connect to other experiments. ]
+There are a couple of very important distinctions to be made between our work and the work of ref. 25 (K.  Kuwahara et al.), which as the referee points out, also identified softening in (c11-c12)/2. First, the data in ref. 25 (figure 2c) appear to be contaminated by the c66 mode, based on the fact that the peak in c66 appears around 60 K. In the work of T. Yanagisawa et al (Journal of the Physical Society of Japan 82 (2013) 013601), the peak is at 130 K, and the elastic constant softens back down to its room-temperature value by T_HO. The data we show in figure 2b, obtained with resonant ultrasound, also shows a maximum at around 130 K, and also softens to its room-temperature value by T_HO. The contamination in ref. 25 is likely an artifact of the pulse-echo ultrasound technique, which can mix between c66 and (c11-c12)/2 when the crystal is not perfectly aligned. Perhaps more importantly, the fit shown in figure 4 of ref 25 does not show very good agreement with the data at any temperature. The model used is one for thermally-populated crystal field levels, and has nothing to do with the phase transition at T_HO. This model does not produce the sharp change in slope of (c11-c12)/2 at T_HO, which is an essential singularity in the thermodynamic free energy and must appear in the elastic moduli, and it does not produce 1/(T-T_0) strain susceptibility above T_HO, which is a signature of strain and order parameter coupling. 
 
 > 3) The agreement of C[B1g] in the region T<T_HO is poor, though only 
 > the cusp at T_HO seems qualitatively consistent with the experiment. 
@@ -123,13 +105,9 @@ This is a consistent with hexadecapolar order
 > does not lead uniquely to the authors' arguments on the realization of 
 > the B1g order parameter. 
 
-The disagreement between the theory at low temperature is resolved by the
-addition of an additional interaction in the mean-field free energy of the form
-ε²η², now shown in Fig. 2 as a thin black line.
+The disagreement between the theory at low temperature is resolved by the addition of an additional interaction in the mean-field free energy of the form ε²η², now shown in Fig. 2 as a thin black line.
 
-While terms like this provide cusp-like features in the modulus for each strain
-symmetry, they cannot explain the 1/ΔT softening seen in the high-temperature
-phase, since their contribution to the response function is zero above T_c.
+While terms like this provide cusp-like features in the modulus for each strain symmetry, they cannot explain the 1/ΔT softening seen in the high-temperature phase, since their contribution to the response function is zero above T_c.
 
 > 4) The most important point in the HO problem is the microscopic 
 > identification of symmetry breaking and the order parameter. In spite 
@@ -140,9 +118,7 @@ phase, since their contribution to the response function is zero above T_c.
 > The authors do not provide any resolution on that point which is the 
 > most relevant in this problem.
 
-The articles below, also cited in our work, all provide experimental evidence
-for the formation of superlattice structure along the c-axis at ambient
-pressure.
+The articles below, also cited in our work, all provide experimental evidence for the formation of superlattice structure along the c-axis at ambient pressure.
 
 [I pulled these from our citation on the estimate for q_*. Do they actually
 provide the evidence we need? Can someone who knows more about these techniques