Swapping, tempering and equi-energy sampling on a selection of models in statistical mechanics [Elektronische Ressource] / vorgelegt Mirko Ebbers

Mirko EbbersSwapping, Tempering andEqui-Energy sampling on aselection of models instatistical mechanics2010MathematikSwapping, Tempering andEqui-Energy sampling on aselection of models instatistical mechanicsInaugural-Dissertationzur Erlangung des Doktorgradesder Naturwissenschaften im FachbereichMathematik und Informatikder Mathematisch-Naturwissenschaftlichen Fakultätder Westfälischen Wilhelms-Universität Münstervorgelegt vonMirko Ebbersaus Düsseldorf2010Dekan Prof. Dr. Matthias LöweErstgutachter Prof. Dr. LöweZweitgutachter Prof. Dr. Gerold AlsmeyerTag der mündlichen Prüfung 27.01.2011Tag der PromotionContentsIntroduction 3Chapter 1. Statistical Mechanics 51. The Curie-Weiss model 62. The Potts model 83. The BEG model 94. Spin glasses 9Chapter 2. Markov-Chain-Monte-Carlo Method 131. Definition of the MCMC Method 132. Technical preparation: Gap and Conductance 143. Metropolis-Hastings Algorithm 154. Torpid mixing of Metropolis in the Curie-Weiss-Model 17Chapter 3. Simulated Tempering and Swapping 211. Simulated Tempering 212. Swapping 223. Known results 244. Technical preparations 27Chapter 4. The Generalized-Curie-Weiss model 291. Defining the Metropolis chain 292. Preparations 303. Result 324. Proof 32Chapter 5. The Blume-Emery-Grifiths model 391. Technical preparations 402. Results 433. Proofs 44Chapter 6. The Random-Energy-Model and the Generalized-del 651. Defining the Metropolis chain 652. Results 663.