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authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-10 12:18:27 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-10 12:18:27 +0100
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Added some bolded comments.
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@@ -286,6 +286,7 @@ the numerator of the Green function gives
\right]
\right\}
\end{equation}
+ \textcolor{red}{\textbf{Not sure if the $N$ belongs here...}}
with sums taken over repeated latin indices.
The average can then be made over $J$ and Hubbard--Stratonovich used to change
variables to replica matrices
@@ -311,6 +312,7 @@ values follows from the jump across the cut, or
\begin{equation}
\rho(\sigma)=\frac1{i\pi}\left(\lim_{\mathop{\mathrm{Im}}\sigma\to0^+}\overline G(\sigma)-\lim_{\mathop{\mathrm{Im}}\sigma\to0^-}\overline G(\sigma)\right)
\end{equation}
+\textcolor{red}{\textbf{Missing a factor of two? Please check...}}
The transition from a one-cut to two-cut singular value spectrum naturally
corresponds to the origin leaving the support of the eigenvalue spectrum.