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| -rw-r--r-- | hidden_order.bib | 14 | ||||
| -rw-r--r-- | main.tex | 3 |
2 files changed, 16 insertions, 1 deletions
diff --git a/hidden_order.bib b/hidden_order.bib index d17c22c..3b779ed 100644 --- a/hidden_order.bib +++ b/hidden_order.bib @@ -500,4 +500,18 @@ thermodynamics from a hidden order parameter.}, file = {/home/pants/Zotero/storage/CDTQB6PI/Inoue et al_2001_High-field magnetization of URu2Si2 under high pressure.pdf;/home/pants/Zotero/storage/323PS9NS/S0921452600006578.html} } +@article{hornreich_critical_1975, + title = {Critical {{Behavior}} at the {{Onset}} of \$\textbackslash{}stackrel\{\textbackslash{}ensuremath\{\textbackslash{}rightarrow\}\}\{\textbackslash{}mathrm\{k\}\}\$-{{Space Instability}} on the \$\textbackslash{}ensuremath\{\textbackslash{}lambda\}\$ {{Line}}}, + volume = {35}, + abstract = {We calculate the critical behavior of systems having a multicritical point of a new type, hereafter called a Lifshitz point, which separates ordered phases with \textrightarrowk=0 and \textrightarrowk{$\not =$}0 along the {$\lambda$} line. For anisotropic systems, the correlation function is described in terms of four critical exponents, whereas for isotropic systems two exponents suffice. Critical exponents are calculated using an {$\epsilon$}-type expansion.}, + number = {25}, + journal = {Physical Review Letters}, + doi = {10.1103/PhysRevLett.35.1678}, + author = {Hornreich, R. M. and Luban, Marshall and Shtrikman, S.}, + month = dec, + year = {1975}, + pages = {1678-1681}, + file = {/home/pants/Zotero/storage/GBYIESIW/Hornreich et al_1975_Critical Behavior at the Onset of.pdf;/home/pants/Zotero/storage/KBYQHWSH/PhysRevLett.35.html} +} + @@ -155,6 +155,7 @@ action of the point group, or \epsilon_\Btg^{(1)}=2\epsilon_{12} \\ \epsilon_\Eg^{(1)}=2\{\epsilon_{11},\epsilon_{22}\}. \end{aligned} + \label{eq:strain-components} \end{equation} Next, all quadratic combinations of these irreducible strains that transform like $\Aog$ are included in the free energy as @@ -183,7 +184,7 @@ If $\X$ is a representation not present in the strain there can be no linear coupling, and the effect of $\eta$ going through a continuous phase transition is to produce a jump in the $\Aog$ strain stiffness. We will therefore focus our attention on order parameter symmetries that produce linear couplings to -strain. +strain. Looking at the components present in \eqref{eq:strain-components}, this rules out all of the u-reps (odd under inversion) and the $\Atg$ irrep as having any anticipatory response in the strain stiffness. If the order parameter transforms like $\Aog$, odd terms are allowed in its free energy and any transition will be abrupt and not continuous without |