From 8268dd6c4a96308b5b8035c9db85296205890131 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 6 May 2020 21:03:50 -0400 Subject: Worked on addressing the fitting questions from the first referee. --- referee_comments.txt | 37 +++++++++++++++++++++++++++++++++++-- 1 file changed, 35 insertions(+), 2 deletions(-) (limited to 'referee_comments.txt') 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 -- cgit v1.2.3-70-g09d2