From 0a73432fb5e4dedb4cac14e9722fe8a26aa69e1a Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 17 Sep 2019 13:34:24 -0400 Subject: defining some variables now that the ginzburg paragraph has been removed --- main.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/main.tex b/main.tex index 98266fc..af39f7f 100644 --- a/main.tex +++ b/main.tex @@ -302,8 +302,8 @@ Near the unordered--modulated transition this yields \end{aligned} \label{eq:susceptibility} \end{equation} -with $\xi_\perp=(|\Delta\tilde r|/D_\perp)^{-1/4}$ and -$\xi_\parallel=(|\Delta\tilde r|/c_\parallel)^{-1/2}$. We must emphasize that +with $\xi_\perp=(|\Delta\tilde r|/D_\perp)^{-1/4}=\xi_{\perp0}|t|^{-1/4}$ and +$\xi_\parallel=(|\Delta\tilde r|/c_\parallel)^{-1/2}=\xi_{\parallel0}|t|^{-1/2}$, where $t=(T-T_c)/T_c$ is the reduced temperature and $\xi_{\perp0}=(D_\perp/aT_c)^{1/4}$ and $\xi_{\parallel0}=(c_\parallel/aT_c)^{1/2}$ are the bare correlation lengths. We must emphasize that this is \emph{not} the magnetic susceptibility because a $\Bog$ or $\Btg$ \op\ cannot couple linearly to a uniform magnetic field. The object defined in \eqref{eq:sus_def} is most readily interpreted as proportional to the two-point @@ -442,7 +442,7 @@ $q_*$ should continuously vanish. Far from the Lifshitz point we expect the wavevector to lock into values commensurate with the space group of the lattice, and moreover that at zero pressure, where the \rus\ data here was collected, the half-wavelength of the modulation should be commensurate with -the lattice, or $q_*\simeq0.328\,\A^{-1}$ \cite{meng_imaging_2013, +the lattice spacing $a_3\simeq9.68\,\A$, or $q_*=\pi/a_3\simeq0.328\,\A^{-1}$ \cite{meng_imaging_2013, broholm_magnetic_1991, wiebe_gapped_2007, bourdarot_precise_2010}. In between these two regimes, the ordering wavevector should shrink by jumping between ever-closer commensurate values in the style of the devil's staircase -- cgit v1.2.3-70-g09d2