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authorkurchan.jorge <kurchan.jorge@gmail.com>2020-12-08 10:34:32 +0000
committeroverleaf <overleaf@localhost>2020-12-08 10:34:46 +0000
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Update on Overleaf.
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diff --git a/bezout.tex b/bezout.tex
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--- a/bezout.tex
+++ b/bezout.tex
@@ -213,12 +213,12 @@ for $\delta=\kappa a^{-(p-2)}$.
Another instrument we have to study this problem is to compute the following partition function:
-\begin{equation}
+\begin{eqnarray}
Z= \int \Pi_i dx_i dy_i \; e^{-\beta_{R} \Re H_0 -\beta_I \Im H_0}
\delta(\sum_i z_i^2-N) \delta\left(\sum_i y_i^2 -N \frac{a-1}{2}\right)
\end{equation}
The energy $\Re H_0, \Im H_0$ are in a one-to one relation with the temperatures $\beta_R,\beta_I$. The entropy $S(a,H_0) = \ln Z+ +\beta_{R} \langle \Re H_0 \rangle +\beta_I \langle \Im H_0\rangle$
-is the logarithm of the number of configurations of a given
+is the logarithm of the number of configurations of a given $(a,H_0)$.
}
\bibliographystyle{apsrev4-2}