Monte Carlo study of the XY-model on quasi-periodic lattices
dc.contributor.author | Reid, R. William. | en_US |
dc.date.accessioned | 2009-07-09T18:39:10Z | |
dc.date.available | 2009-07-09T18:39:10Z | |
dc.date.issued | 1996-07-09T18:39:10Z | |
dc.identifier.uri | http://hdl.handle.net/10464/1970 | |
dc.description.abstract | Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Brock University | en_US |
dc.subject | Quasicrystals | en_US |
dc.subject | Monte Carlo method. | en_US |
dc.subject | Lattice theory. | en_US |
dc.title | Monte Carlo study of the XY-model on quasi-periodic lattices | en_US |
dc.type | Electronic Thesis or Dissertation | en |
dc.degree.name | M.Sc. Physics | en_US |
dc.degree.level | Masters | en_US |
dc.contributor.department | Department of Physics | en_US |
dc.degree.discipline | Faculty of Mathematics and Science | en_US |
refterms.dateFOA | 2021-08-07T02:01:00Z |