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| -rw-r--r-- | bezout.tex | 5 |
1 files changed, 4 insertions, 1 deletions
@@ -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 |