Introduction to Monte Carlo methods for an Ising Model of a Ferromagnet
| dc.creator | Kotze, Jacques | |
| dc.date | 2008-03-03 | |
| dc.date.accessioned | 2026-07-07T09:24:21Z | |
| dc.date.available | 2026-07-07T09:24:21Z | |
| dc.description | This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in particular the applicability of the Metropolis-Hastings algorithm. Importantly the potentially devastating effects of spontaneous magnetization are highlighted and a means to avert this is examined. An Ising model is introduced and used to investigate the properties of a two dimensional ferromagnet with respect to its magnetization and energy at varying temperatures. The observables are calculated and a phase transition at a critical temperature is also illustrated and evaluated. Lastly a finite size scaling analysis is undertaken to determine the critical exponents and the Curie temperature is calculated using a ratio of cumulants with differing lattice sizes. The results obtained from the simulation are compared to exact calculations to endorse the validity of this numerical process. A copy of the code used, written in C++, is enclosed and is freely available for use and modification under the General Public License. | |
| dc.description | 26 pages, 21 figures, conference presentation at SASNAM 2003, Honours project 2001 | |
| dc.identifier | https://arxiv.org/abs/0803.0217 | |
| dc.identifier | http://arxiv.org/abs/0803.0217 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156062 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Materials Science | |
| dc.title | Introduction to Monte Carlo methods for an Ising Model of a Ferromagnet | |
| dc.type | text |