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| -rw-r--r-- | main.tex | 12 |
1 files changed, 6 insertions, 6 deletions
@@ -213,7 +213,7 @@ with $r\to\tilde r=r-b^2/4\lambda_\X$. With the strain traced out \eqref{eq:fo} describes the theory of a Lifshitz point at $\tilde r=c_\perp=0$ \cite{lifshitz_theory_1942, -lifshitz_theory_1942-1}. For a scalar order parameter ($\Bog$ or $\Btg$) it is +lifshitz_theory_1942-1}. For a one-component order parameter ($\Bog$ or $\Btg$) it is traditional to make the field ansatz $\eta(x)=\eta_*\cos(q_*x_3)$. For $\tilde r>0$ and $c_\perp>0$, or $\tilde r<c_\perp^2/4D_\perp$ and $c_\perp<0$, the only stable solution is $\eta_*=q_*=0$ and the system is unordered. For $\tilde @@ -226,9 +226,9 @@ $q_*^2=-c_\perp/2D_\perp$ and =\frac{\tilde r_c-\tilde r}{3u} \end{equation} with $\tilde r_c=c_\perp^2/4D_\perp$ and the system has modulated order. The -transition between the uniform and modulated orderings is abrupt for a scalar +transition between the uniform and modulated orderings is abrupt for a one-component field and occurs along the line $c_\perp=-2\sqrt{-D_\perp\tilde r/5}$. For a -vector order parameter ($\Eg$) we must also allow a relative phase between the +two-component order parameter ($\Eg$) we must also allow a relative phase between the two components of the field. In this case the uniform ordered phase is only stable for $c_\perp>0$, and the modulated phase is now characterized by helical order with $\eta(x)=\eta_*\{\cos(q_*x_3),\sin(q_*x_3)\}$ and @@ -249,9 +249,9 @@ diagrams for this model are shown in Figure \ref{fig:phases}. \caption{ Phase diagrams for (a) \urusi\ from experiments (neglecting the superconducting phase) \cite{hassinger_temperature-pressure_2008} (b) mean - field theory of a scalar ($\Bog$ or $\Btg$) Lifshitz point (c) mean field - theory of a vector ($\Eg$) Lifshitz point. Solid lines denote continuous - transitions, while dashed lines denote abrupt transitions. + field theory of a one-component ($\Bog$ or $\Btg$) Lifshitz point (c) mean + field theory of a two-component ($\Eg$) Lifshitz point. Solid lines denote + continuous transitions, while dashed lines denote abrupt transitions. } \label{fig:phases} \end{figure} |