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| -rw-r--r-- | marginal.tex | 5 |
1 files changed, 2 insertions, 3 deletions
diff --git a/marginal.tex b/marginal.tex index 45d65dc..bc7c4ab 100644 --- a/marginal.tex +++ b/marginal.tex @@ -329,7 +329,7 @@ Extremizing this action over the new parameters $y$, $\Delta z$, and $\hat\lambd -\frac{\mu-\lambda^*}{2\sigma}\sqrt{\left(\frac{\mu-\lambda^*}{2\sigma}\right)^2-1} \right] \end{align} -Inserting this solution into $\mathcal S_\infty$ we find +Inserting this solution into the effective action we find \begin{equation} \label{eq:goe.large.dev} \begin{aligned} &G_{\lambda^*}(\mu) @@ -342,8 +342,7 @@ Inserting this solution into $\mathcal S_\infty$ we find \end{aligned} \end{equation} This function is plotted in Fig.~\ref{fig:large.dev} for $\lambda^*=0$. For $\mu<2\sigma$ $G_{0}(\mu)$ has an -imaginary part. This indicates that the existence of a marginal minimum for this -parameter value corresponds with a large deviation that grows faster than $N$, +imaginary part. This indicates that the existence of a minimally zero eigenvalue when $\mu<2\sigma$ corresponds with a large deviation that grows faster than $N$, rather like $N^2$, since in this regime the bulk of the typical spectrum is over zero and therefore extensively many eigenvalues have to have large deviations in order for the smallest eigenvalue to be zero. For |