ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The magnetization of ultrathin films shows a power law dependence on temperature with an exponent β that depends on the spin anisotropy. Experimentally it is found that films with easy-axis anisotropy show β=1/8, characteristic of the two-dimensional Ising model, while those with dominant easy-plane anisotropy show β=0.23. We recently discussed the finite size magnetization of the XY model and showed that this system has universal behavior which leads to the exponent β=0.23. A number of authors have therefore interpreted their results in terms of the finite size two-dimensional XY model. The success of these explanations implies that the four- and sixfold anisotropy fields present in real films are irrelevant in determining the critical behavior of the magnetization. In the sixfold case this observation agrees with theoretical expectations, while in the fourfold case the situation is unclear, as the renormalization group analysis of José et al. shows the fourfold field to be a marginally relevant variable which gives rise to nonuniversal exponents. This theoretical result, however, pertains to the thermodynamic limit and is not necessarily relevant to real finite systems. We investigate the effect of symmetry breaking fields on the magnetic behavior of idealized finite size XY models by means of Monte Carlo simulation. We find that the fourfold field is indeed irrelevant for the system sizes of interest, and may only become relevant for system sizes beyond the physical domain. We also confirm that the sixfold field is both qualitatively and quantitatively irrelevant, and notice a number of novel features connected with the behavior of finite size models which cannot be observed in the thermodynamic limit. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.361859
