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Simulational methods in Physics
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Critical Phenomena
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Script
Critical Phenomena
Jan Martin Pawlowski,
winter term 2010/2011
Script
1 Introduction
1.1 Ferromagnetic transition
1.2 Ising model
1.3 Mean-Field approximation & critical exponents
1.4 Correlation functions
2 Landau theory
2.1 Ginzburg-Landau hamiltonian
2.2 Phase transitions
2.3 Correlation functions
2.4 Fluctuations & Ginzburg criterion
3 Renormalisation group
3.1 Block-spin transformations & coarse-graining
3.2 Critical exponents & scaling
3.3 Approximation by cumulants
4 Functional renormalisation
4.1 Flow equation
4.2 Perturbation theory
4.3 Effective Potential approximation
4.4 RG-equations, anomalous dimensions & critical phenomena
5 O(N)-models & critical phenomena
5.1 O(N)-symmetric scalar theories
5.2 Functional RG for the O(N)-model
5.3 1/N-Expansion