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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-10 13:52:25 +0100 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-10 13:52:25 +0100 |
commit | 68045a697a427f7ff8745fbf6a1fbfce0f0acc72 (patch) | |
tree | b77f5c72d57c686dd2b32315a62a11009f055b00 | |
parent | 3400a6a591e6e3207a9d8964ad02f7578c1db0d8 (diff) | |
parent | 59ff2b9c61517ac7f89f38821a09ca4cf9ac28cd (diff) | |
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Merge branch 'master' of https://git.overleaf.com/5fcce4736e7f601ffb7e1484
-rw-r--r-- | bezout.tex | 6 |
1 files changed, 3 insertions, 3 deletions
@@ -111,9 +111,9 @@ $\epsilon=H/N$, the average energy. Critical points are given by the set of equations: \begin{equation} -\frac{c_p}{(p-1)!}\sum_{ i, i_2\cdots i_p}^NJ_{i, i_2\cdots i_p}z_{i_2}\cdots z_{i_p} = \epsilon z_ - - +\frac{c_p}{(p-1)!}\sum_{ i, i_2\cdots i_p}^NJ_{i, i_2\cdots i_p}z_{i_2}\cdots z_{i_p} = \epsilon z_i +\end{equation} +which for given $\epsilon$ are a set pf $N$ equations of degree $ Since $H$ is holomorphic, a point is a critical point of its real part if and only if it is also a critical point of its imaginary part. The number of critical points of $H$ is therefore the number of critical points of |