\select@language {german}
\contentsline {chapter}{\numberline {1}Monte-Carlo-Simulationen des Ising-Modells}{1}{chapter.1}
\contentsline {section}{\numberline {1.1}Statistische Eigenschaften von Zeitreihen}{2}{section.1.1}
\contentsline {subsection}{\numberline {1.1.1}Motivation}{2}{subsection.1.1.1}
\contentsline {section}{\numberline {1.2}Metropolis Monte-Carlo Methode}{6}{section.1.2}
\contentsline {section}{\numberline {1.3}Statistische Physik im kanonischen Ensemble}{11}{section.1.3}
\contentsline {section}{\numberline {1.4}Das Ising-Modell}{12}{section.1.4}
\contentsline {subsection}{\numberline {1.4.1}Mean-field solution of the Ising model}{13}{subsection.1.4.1}
\contentsline {subsection}{\numberline {1.4.2}Ising model: solution in 1 dimension}{14}{subsection.1.4.2}
\contentsline {subsection}{\numberline {1.4.3}Ising model on the 2d square lattice}{15}{subsection.1.4.3}
\contentsline {subsection}{\numberline {1.4.4}Ising model: simulation}{15}{subsection.1.4.4}
\contentsline {subsection}{\numberline {1.4.5}Metropolis importance sampling Monte Carlo scheme}{15}{subsection.1.4.5}
\contentsline {subsection}{\numberline {1.4.6}Ising-Modell (NN-Wechselwirkung) - Kritische Temperaturen}{16}{subsection.1.4.6}
\contentsline {subsection}{\numberline {1.4.7}Kritische Exponenten des Ising-Modells in d=3}{17}{subsection.1.4.7}
\contentsline {section}{\numberline {1.5}Finite-size scaling}{17}{section.1.5}
\contentsline {section}{\numberline {1.6}Cluster-MC-Algorithmen}{19}{section.1.6}
\contentsline {subsection}{\numberline {1.6.1}Swendson-Wang Cluster-Update-Algorithmus}{20}{subsection.1.6.1}
\contentsline {chapter}{\numberline {2}Exakte Diagonalisierung}{23}{chapter.2}
\contentsline {section}{\numberline {2.1}Matrixdarstellung des Heisenberg-Modells}{24}{section.2.1}
\contentsline {section}{\numberline {2.2}Mathematischer Exkurs: Eigenwertprobleme}{26}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}Allgemeine Aussagen}{27}{subsection.2.2.1}
\contentsline {section}{\numberline {2.3}Reduktion des Hilbertraums (vor ED)}{28}{section.2.3}