From: hackbard Date: Mon, 26 May 2003 17:23:04 +0000 (+0000) Subject: somefixes X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f6b9e9169e846fb7b7fd77df9293499291d04354;p=lectures%2Flatex.git somefixes --- diff --git a/ising/ising_slides.tex b/ising/ising_slides.tex index acd4553..29a7926 100644 --- a/ising/ising_slides.tex +++ b/ising/ising_slides.tex @@ -128,7 +128,10 @@ Molekularfeldn"aherung:\\ Approximation: Vernachl"assigung der Spinfluktuationen $S_i-$\\ Spin-Wechselwirkungs-Term: \[ - S_iS_j = (S_i-m+m)(S_j-m+m)=m^2+m(S_i-m)+m(S_j-m)+(S_i-m)(S_j-m) +\begin{array}{ll} + S_iS_j & = (S_i-m+m)(S_j-m+m)\\ + & = m^2+m(S_i-m)+m(S_j-m)+(S_i-m)(S_j-m) +\end{array} \] wobei: \begin{itemize} @@ -282,7 +285,7 @@ Die Matrix muss also wie folgt aussehen: Zustandssumme: \[ \begin{array}{ll} - \displaystyle Z & \displaystyle = \sum_{S_1} \sum_{S_2} \ldots \sum_{S_N} \ldots \\[2mm] + \displaystyle Z & \displaystyle = \sum_{S_1} \sum_{S_2} \ldots \sum_{S_N} \ldots \\[2mm] \displaystyle & \displaystyle = \sum_{S_1} \\[2mm] \displaystyle & \displaystyle = \textrm{Sp} \, \mathbf{T}^N \end{array} @@ -349,7 +352,7 @@ Erkenntnis: \end{itemize} F"ur $T=0$: \[ - \lim_{T \rightarrow 0} \frac{\lambda_+}{\lambda_-}=1 \, \textrm{obere Approximation nichtmehr g"ultig)} + \lim_{T \rightarrow 0} \frac{\lambda_+}{\lambda_-}=1 \, \textrm{, ist obere Approximation nichtmehr g"ultig} \] Phasen"ubergang bei $B_0=T=0$ (Korrelationsl"ange geht gegen unendlich)\\ Kritische Exponenten: @@ -497,7 +500,7 @@ somit gilt: \begin{slide} Realisierung einer Boltzmannverteilung: Metropolis Algorithmus\\ -$[4]$ http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/index.html +$[4]$ http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/ \[ W(A \rightarrow B) = \left\{ \begin{array}{ll} @@ -608,7 +611,7 @@ Spingl"aser: Optimierung und Ged"achtnis \item \label{lit1} W. Nolting, Grundkurs: Statistische Physik, Band 6 \item \label{lit2} Rodney J. Baxter, Exactly Solved Models in Statistical Mechanics \item \label{lit3} http://www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture\_26/node2.html -\item \label{lit4} http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/index.html +\item \label{lit4} http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/ \item \label{lit5} Hildegard Meyer-Ortmanns, Abstract: Immigration, integration and ghetto formation \item \label{lit6} K. Malarz, Abstract: Social phase transition in Solomon network \item \label{lit7} Kerson Huang, Statistical mechanics