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\centerline{\bf \Large Possible projects for visit in Chennai}
\subsection*{Kosterlitz-Thouless related rare-region projects}
\begin{itemize}
\item Griffiths effects at the classical Kosterlitz-Thouless transition. These are
presumably weak in the thermodynamics , so this is a warmup calculation.
Maybe something interesting happens in the classical dynamics (long-time
behavior in the autocorrelation function).
\item The next step would be O(2) in 1+1 d. I believe this has been done by
Gil Refael et al a while ago.
\item A really interesting case, in my opinion would be a randomly layered
O(2) system. Each layer could have a KT transition at some T. What happens
if these layers are weakly coupled? This would be relevant for layered
superconductors. Here one would need to understand how two KT layers merge.
\end{itemize}
\subsection*{QPT with disorder and non-Ohmic dissipation}
This is a generalization of the work I did with Jose and Chetan. What happens with the
reansition if your O(N) order parameter is coupled not to an Ohmic bath but to a
non-Ohmic bath. (In the Ohmic case you get an infinite-randomness critical point.)
\begin{itemize}
\item One could first work out the form of the Griffiths singularities using the usual
optimal fluctuation arguments.
\item More interesting is how the strong disorder-renormalization group changes
in these cases. We already have the recursion relations for a single RG step,
but we do not yet have derived the flow equations or solved them. This project has
the advantage that it is clear what needs to be done technically (but it may be
hard ...).
\end{itemize}
\subsection*{First-order QPT with disorder}
Question is what happens to a 1st order QPT when it is destroyed by disorder (in
particular in 2d). As far as I know there is just this Chakravarty paper. We should start
by identifying simple first order QPTs, add disorder and study by RG. Ideal are
fluctuation driven first-order transitions because we can control the flow at weak
disorder but even strong-first order transitions are OK, because we could apply the
strong disorder renormalization group.
\subsection*{Further ideas in no particular order}
\begin{itemize}
\item Destruction (?) of an electronic nematic by disorder in analogy to the destruction
of non-s-wave SC. Has this been doe already? If not, it should be a
straight-forward perturbative calculation of the appropriate two-point vertex.
\end{itemize}
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