Update on Overleaf.

3 files changed, 37 insertions, 23 deletions

diff --git a/hidden_order.bib b/hidden_order.bib
index cc404a0..45bb709 100644
--- a/hidden_order.bib
+++ b/hidden_order.bib
@@ -770,4 +770,15 @@ Raman spectroscopy is used to uncover an unusual ordering in the low-temperature
   file = {/home/pants/.zotero/data/storage/UJTH89KV/Yanagisawa - 2014 - Ultrasonic study of the hidden order and heavy-fer.pdf}
 }
 
+@article{ghiringhelli2012long,
+  title={Long-range incommensurate charge fluctuations in (Y, Nd) Ba2Cu3O6+ x},
+  author={Ghiringhelli, G and Le Tacon, M and Minola, Matteo and Blanco-Canosa, S and Mazzoli, Claudio and Brookes, NB and De Luca, GM and Frano, A and Hawthorn, DG and He, F and others},
+  journal={Science},
+  volume={337},
+  number={6096},
+  pages={821--825},
+  year={2012},
+  publisher={American Association for the Advancement of Science}
+}
+
 
diff --git a/library.bib b/library.bib
index c944258..6544ee6 100644
--- a/library.bib
+++ b/library.bib
@@ -3222,3 +3222,14 @@ I don't see how this is any better for classical systems and I don't see how it
 	Year = {1985},
 	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.32.6920},
 	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.32.6920}}
+	
+@article{ghiringhelli2012long,
+  title={Long-range incommensurate charge fluctuations in (Y, Nd) Ba2Cu3O6+ x},
+  author={Ghiringhelli, G and Le Tacon, M and Minola, Matteo and Blanco-Canosa, S and Mazzoli, Claudio and Brookes, NB and De Luca, GM and Frano, A and Hawthorn, DG and He, F and others},
+  journal={Science},
+  volume={337},
+  number={6096},
+  pages={821--825},
+  year={2012},
+  publisher={American Association for the Advancement of Science}
+}
diff --git a/main.tex b/main.tex
index fbb5e48..9d086c4 100644
--- a/main.tex
+++ b/main.tex
@@ -496,7 +496,7 @@ corresponding modulus.
 
 \section{Comparison to experiment}
 \Rus\ experiments~\cite{ghosh_single-component_nodate} yield the individual
-elastic moduli broken into irrep symmetries; data for the $\Bog$ and $\Btg$
+elastic moduli broken into irreps; data for the $\Bog$ and $\Btg$
 components defined in \eqref{eq:strain-components} are shown in Figures
 \ref{fig:data}(a--b).  The $\Btg$ in Fig.~\ref{fig:data}(a) modulus doesn't
 appear to have any response to the presence of the transition, exhibiting the
@@ -546,44 +546,36 @@ pressure, where the depth of the cusp in the $\Bog$ modulus should deepen
 (perhaps with these commensurability jumps) at low pressure and approach zero
 as $q_*^4\sim(c_\perp/2D_\perp)^2$ near the Lifshitz point. 
 Alternatively, \rus\ done at ambient pressure might examine the heavy Fermi
-liquid to \afm\ transition by doping. Though previous \rus\ studies have doped
-\urusi\ with Rhodium,\cite{yanagisawa_ultrasonic_2014} the magnetic rhodium dopants likely promote magnetic phases. A non-magnetic dopant such as phosphorous may more faithfully explore
-the transition out of the HO phase. Our work also motivates experiments
+liquid to \afm\ transition by doping. Our work also motivates experiments
 that can probe the entire correlation function---like x-ray and neutron
 scattering---and directly resolve its finite-$q$ divergence.  The presence of
 spatial commensurability is known to be irrelevant to critical behavior at a
 one-component disordered to modulated transition, and therefore is not
-expected to modify the thermodynamic behavior
-otherwise.\cite{garel_commensurability_1976} 
+expected to otherwise modify the thermodynamic behavior.\cite{garel_commensurability_1976} 
 
 There are two apparent discrepancies between the orthorhombic strain in the
-phase diagram presented by recent x-ray data\cite{choi_pressure-induced_2018}
-and that predicted by our mean field theory when its uniform ordered phase is
+phase diagram presented by recent x-ray data\cite{choi_pressure-induced_2018},
+and that predicted by our mean field theory if its uniform $\Bog$ phase is
 taken to be coincident with \urusi's \afm.  The first is the apparent onset of
-the orthorhombic phase in the \ho\ state prior to the onset of \afm.  As the
-recent x-ray research\cite{choi_pressure-induced_2018} notes, this could be due
+the orthorhombic phase in the \ho\ state at slightly lower pressures than the onset of \afm.  As the
+recent x-ray research\cite{choi_pressure-induced_2018} notes, this misalignment of the two transitions as function of doping could be due
 to the lack of an ambient pressure calibration for the lattice constant. The
 second discrepancy is the onset of orthorhombicity at higher temperatures than
-the onset of \afm.  Susceptibility data sees no trace of another phase
-transition at these higher temperatures.\cite{inoue_high-field_2001} We suspect
-that the high-temperature orthorhombic signature is not the result of a bulk
-phase, and could be due to the high energy (small-wavelength) nature of x-rays
-as an experimental probe: \op\ fluctuations should lead to the formation of
-orthorhombic regions on the order of the correlation length that become larger
-and more persistent as the transition is approached. 
+the onset of \afm. We note that magnetic susceptibility data sees no trace of another phase
+transition at these higher temperatures. \cite{inoue_high-field_2001} It is therefore possible that the high-temperature orthorhombic signature in x-ray scattering is not the result of a bulk thermodynamic phase, but instead marks the onset of short-range correlations, as it does in the high-T$_{\mathrm{c}}$ cuprates \cite{ghiringhelli2012long} (where the onset of CDW correlations also lacks a thermodynamic phase transition). 
 
 Three dimensions is below the upper critical dimension $4\frac12$ of a
-one-component disordered to modulated transition, and so mean field theory
+one-component disordered-to-modulated transition, and so mean field theory
 should break down sufficiently close to the critical point due to fluctuations,
 at the Ginzburg temperature. \cite{hornreich_lifshitz_1980,
-ginzburg_remarks_1961} Magnetic phase transitions tend to have Ginzburg
+ginzburg_remarks_1961} Magnetic phase transitions tend to have a Ginzburg
 temperature of order one.  Our fit above gives $\xi_{\perp0}q_*=(D_\perp
 q_*^4/aT_c)^{1/4}\simeq2$, which combined with the speculation of
 $q_*\simeq\pi/a_3$ puts the bare correlation length $\xi_{\perp0}$ at about
 what one would expect for a generic magnetic transition.  The agreement of this
 data in the $t\sim0.1$--10 range with the mean field exponent suggests that
 this region is outside the Ginzburg region, but an experiment may begin to see
-deviations from mean field behavior within around several degrees Kelvin of the
+deviations from mean field behavior within approximately several Kelvin of the
 critical point. An ultrasound experiment with more precise temperature
 resolution near the critical point may be able to resolve a modified cusp
 exponent $\gamma\simeq1.31$,\cite{guida_critical_1998} since the universality
@@ -613,10 +605,10 @@ uniform $\Bog$ electronic order.
 The corresponding prediction of uniform $\Bog$ symmetry breaking in the high
 pressure phase is consistent with recent diffraction experiments,
 \cite{choi_pressure-induced_2018} except for the apparent earlier onset in
-temperature of the $\Bog$ symmetry breaking, which we believe to be due to
-fluctuating order above the actual phase transition.  This work motivates both
+temperature of the $\Bog$ symmetry breaking, which we believe may be due to
+fluctuating order at temperatures above the actual transition temperature.  This work motivates both
 further theoretical work regarding a microscopic theory with modulated $\Bog$
-order, and preforming \rus\ experiments at pressure that could further support
+order, and preforming symmetry-sensitive thermodynamic experiments at pressure, such as ultrasound, that could further support
 or falsify this idea.
 
 \begin{acknowledgements}