From e2084b32773fb240239e70c28956fff9ee370f14 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Tue, 8 Dec 2020 10:32:48 +0000 Subject: Update on Overleaf. --- bezout.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/bezout.tex b/bezout.tex index 621a52f..a7db520 100644 --- a/bezout.tex +++ b/bezout.tex @@ -218,7 +218,7 @@ Another instrument we have to study this problem is to compute the following par \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 thnumber of configurations of a given +is the logarithm of the number of configurations of a given } \bibliographystyle{apsrev4-2} -- cgit v1.2.3-70-g09d2 From 3bfcc79839e9311f9ca8d1ffac439922c542be86 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Tue, 8 Dec 2020 10:34:32 +0000 Subject: Update on Overleaf. --- bezout.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/bezout.tex b/bezout.tex index a7db520..8115df9 100644 --- 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} -- cgit v1.2.3-70-g09d2 From d1a667025fb04971f7e03aac4ac4f970bc7a6210 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Tue, 8 Dec 2020 10:34:49 +0000 Subject: Update on Overleaf. --- bezout.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/bezout.tex b/bezout.tex index 8115df9..f07374a 100644 --- a/bezout.tex +++ b/bezout.tex @@ -216,7 +216,7 @@ Another instrument we have to study this problem is to compute the following par \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} +\end{eqnarray} 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 $(a,H_0)$. -- cgit v1.2.3-70-g09d2