diff options
| -rw-r--r-- | hidden_order.bib | 10 | ||||
| -rw-r--r-- | main.tex | 6 |
2 files changed, 8 insertions, 8 deletions
diff --git a/hidden_order.bib b/hidden_order.bib index e2ed334..3ae6931 100644 --- a/hidden_order.bib +++ b/hidden_order.bib @@ -185,7 +185,7 @@ Ultrasound Spectroscopy and Machine Learning}, issn = {0036-8075} } -@article{Ginzburg_1961, +@article{Ginzburg_1961_Some, author = {Ginzburg, Vitaly Lazarevich}, title = {Some Remarks on Phase Transitions of the Second Kind and the Microscopic theory of Ferroelectric Materials}, journal = {Soviet Physics, Solid State}, @@ -196,13 +196,13 @@ Ultrasound Spectroscopy and Machine Learning}, url = {https://ci.nii.ac.jp/naid/10010072128/} } -@article{Guida_1998, +@article{Guida_1998_Critical, author = {Guida, R. and Zinn-Justin, Jean}, title = {Critical exponents of the {$N$}-vector model}, journal = {Journal of Physics A: Mathematical and General}, publisher = {IOP Publishing}, year = {1998}, - month = {October}, + month = {10}, number = {40}, volume = {31}, pages = {8103--8121}, @@ -404,7 +404,7 @@ Ultrasound Spectroscopy and Machine Learning}, doi = {10.1143/jpsj.66.3251} } -@article{Lifshitz_1942a, +@article{Lifshitz_1942_OnI, author = {Lifshitz, Evgeniĭ Mikhaĭlovich}, title = {On the theory of phase transitions of the second order {I}}, journal = {Proceedings of the USSR Academy of Sciences Journal of Physics}, @@ -414,7 +414,7 @@ Ultrasound Spectroscopy and Machine Learning}, subtitle = {Changes of the elementary cell of a crystal in phase transitions of the second order} } -@article{Lifshitz_1942b, +@article{Lifshitz_1942_OnII, author = {Lifshitz, Evgeniĭ Mikhaĭlovich}, title = {On the theory of phase transitions of the second order {II}}, journal = {Proceedings of the USSR Academy of Sciences Journal of Physics}, @@ -286,7 +286,7 @@ to $f_\op$ with the identification $r\to\tilde r=r-b^2/2C^0_\X$. \end{figure} With the strain traced out, \eqref{eq:fo} describes the theory of a Lifshitz -point at $\tilde r=c_\perp=0$.\cite{Lifshitz_1942a, Lifshitz_1942b} The +point at $\tilde r=c_\perp=0$.\cite{Lifshitz_1942_OnI, Lifshitz_1942_OnII} The properties discussed in the remainder of this section can all be found in a standard text, e.g., in chapter 4 \S6.5 of Chaikin \& Lubensky.\cite{Chaikin_1995} For a one-component \op\ ($\Bog$ or $\Btg$) and @@ -579,7 +579,7 @@ 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 should break down sufficiently close to the critical point due to fluctuations, -at the Ginzburg temperature. \cite{Hornreich_1980, Ginzburg_1961} Magnetic +at the Ginzburg temperature. \cite{Hornreich_1980, Ginzburg_1961_Some} 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 @@ -589,7 +589,7 @@ 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 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_1998} since the +resolve a modified cusp exponent $\gamma\simeq1.31$,\cite{Guida_1998_Critical} since the universality class of a uniaxial modulated one-component \op\ is $\mathrm O(2)$.\cite{Garel_1976} We should not expect any quantitative agreement between mean field theory and experiment in the low temperature phase since, by the |