Monte Carlo simulations used for representing dynamical physical phenomena are studied in terms of a Markov chain operator acting on the probability distrubution of the states of a given system. The most general transition rule satisfying detailed balance and leading to a canonical ensemble probability distribution is derived using this formalism. The explicit Markov chain representing the two most commonly used canonical algorithms, the Metropolis and the Glauber transition rules, is then constructed and numerically applied to the states of an Ising model. The dynamical properties of the system are studied for each algorithm. Various measures, such as time-time correlation functions, are estimated for different system sizes and finite-size sealing is applied. In particular, the effects of the transition rule on the dynamic critical exponent is investigated. / We at first examine one- and two-dimensional systems using periodic boundary conditions. Systems with free boundary conditions were also studied, and their results were equivalent with respect to the dynamical critical properties of the system. The effects of conservation laws were also investigated and both conserved and non-conserved systems were studied. Both local and non-local spin-exchange dynamics were investigated for conserved systems. Finally, our approach was used to simulate quenches on small systems. / This method is them used to analyze phenomenological transformations done by dynamical renormalization-group (RG) methods. It is found that, when the RG transformation is linear in probability space, there exists a corresponding Markov chain generating the time sequence of the renormalized systems. An example is given for the one-dimensional Ising model.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.28814 |
| Date | January 1994 |
| Creators | Lacasse, Martin Daniel |
| Contributors | Grant, Martin (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001461483, proquestno: NN05740, Theses scanned by UMI/ProQuest. |
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