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-rw-r--r--bezout.tex5
1 files changed, 4 insertions, 1 deletions
diff --git a/bezout.tex b/bezout.tex
index ce3e850..e4aead7 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -43,7 +43,10 @@ The most tractable family of these are the mean-field spherical p-spin models d
\begin{equation} \label{eq:bare.hamiltonian}
E = \sum_p \frac{c_p}{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p},
\end{equation}
-where the $J_{i_1\cdots i_p}$ are
+where the $J_{i_1\cdots i_p}$ are real Gaussian variables and the $z_i$ are real and constrained
+to a sphere $\sum_i z_i^2=N$.
+
+In th
where $z\in\mathbb C^N$ is constrained by $z^2=N$ and $J$ is a symmetric tensor
whose elements are complex normal with $\langle|J|^2\rangle=p!/2N^{p-1}$ and
$\langle J^2\rangle=\kappa\langle|J|^2\rangle$ for complex parameter