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Titlebook: Computational Statistical Physics; From Billiards to Mo Karl Heinz Hoffmann,Michael Schreiber Book 2002 Springer-Verlag Berlin Heidelberg 2

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,Aperiodicity and Disorder — Do They Play a Role?,sed on scaling arguments as well as specific results for Ising models with random disorder or certain kinds of aperiodic order are reviewed. In particular, this includes an exact real-space renormalization treatment of the Ising quantum chain with coupling constants modulated according to substituti
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Quantum Phase Transitions,They are caused by quantum fluctuations which are a consequence of Heisenberg’s uncertainty principle. These lecture notes give a pedagogical introduction to quantum phase transitions. After collecting a few basic facts about phase transitions and critical behavior we discuss the importance of quant
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Introduction to Energy Level Statistics, the repulsion of energy levels is discussed. The importance of the symmetries of the system for level repulsion is emphasized. Several recent physical examples of level statistics of disordered quantum coherent systems are discussed including localized and metallic systems, the universal behaviour
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Percolation, Renormalization and Quantum Hall Transition,prominent algorithms devised to study percolation numerically. The real-space renormalization group treatment of the percolation problem is then discussed. As a rather novel application of this approach to percolation, I will review recent results using similar real-space renormalization ideas that
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https://doi.org/10.1007/978-1-349-26211-3 prediction error, antipredictable sequences, interacting perceptrons and application to the minority game are discussed. Finally, as a demonstration, a perceptron predicts bit sequences produced by human beings.
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Michele Mäder,Manfred Kirchgeorgprominent algorithms devised to study percolation numerically. The real-space renormalization group treatment of the percolation problem is then discussed. As a rather novel application of this approach to percolation, I will review recent results using similar real-space renormalization ideas that have been applied to the quantum Hall transition.
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