The numerical calculation of the partition function of the 3d Ising model and the 2d XY model are performed using the newly developed Spectral Density method. The performance and utility of the method are also shown. The finite size scaling of the complex zeros of the partition function is used to estimate the critical exponent $\nu$ for the two models. Good estimates of $\nu$ exist for the 3d Ising model and are found to agree with the estimates calculated here. Recently, there has been debate over whether the XY model has an infinite order phase transition as previously believed or a finite order transition. The critical exponent $\nu$ is sensitive to this question. Unlike a finite order transition, it is impossible to define $\nu$ for an infinite order transition. It is shown that if estimates of $\nu$ are measured for an infinite order transition, the estimates will diverge in the thermodynamic limit. The nature of the XY model's phase transition is explored by finding estimates of $\nu$ and the behavior of the derivatives of the free energy; however, the results are inconclusive. / Source: Dissertation Abstracts International, Volume: 50-08, Section: B, page: 3549. / Major Professor: Dennis W. Duke. / Thesis (Ph.D.)--The Florida State University, 1989.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_78060 |
| Contributors | Carter, Paul Alan., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 169 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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