final fixes (hopefully)

[lectures/latex.git] / ising / ising_slides.tex

diff --git a/ising/ising_slides.tex b/ising/ising_slides.tex
index a52fed7..acd4553 100644 (file)
--- a/ising/ising_slides.tex
+++ b/ising/ising_slides.tex
@@ -169,8 +169,8 @@ implizite Bestimmungsgleichung f"ur $B_0=0$:
 
 \begin{slide}
 \begin{itemize}
-\item L"osung: $m \neq 0 \longleftrightarrow \frac{\partial (\tanh (\beta Jm))}{\partial m} > 1$ bei $m=0$
-\item kritische Temperatur: $\frac{\partial (\tanh (\beta Jm))}{\partial m} = 1$ bei $m=0$
+\item L"osung: $m \neq 0 \longleftrightarrow \frac{\partial (\tanh (\beta Jm))}{\partial m} > 1$
+\item kritische Temperatur: $\frac{\partial (\tanh (\beta Jm))}{\partial m} = 1$ f"ur $m=0$
 \end{itemize}
 % \setlength{\unitlength}{2cm}
 % \begin{picture}(6,4)(-3,-2)
@@ -305,7 +305,7 @@ F"ur den Fall $B_0 = 0$ gilt:
 \[
  \begin{array}{l}
   \displaystyle \lambda_{\pm} = e^K \pm e^{-K} \\[2mm]
-  \displaystyle Z = 2^N \cosh^N (K) + 2^N \sinh^N (K) = 2^N \cosh^N (K) (1 + \tanh^N (K)) \stackrel{N >> 1}{\longrightarrow} 2^N \cosh^N (K) \\[2mm]
+  \displaystyle Z = 2^N \cosh^N (K) + 2^N \sinh^N (K) \stackrel{N >> 1}{\longrightarrow} 2^N \cosh^N (K) \\[2mm]
   \displaystyle F = -k_B T \, \textrm{ln} \, Z \stackrel{N >> 1}{\longrightarrow} -N k_B T \, \textrm{ln} \, (2 \cosh (\beta J))
  \end{array}
 \]