University of Twente Student Theses
The effect of an external magnetic field on an antiferromagnetic two-dimensional square Ising model with anisotropic nearest neighbour interaction
Rorink, W.F.G. (2024) The effect of an external magnetic field on an antiferromagnetic two-dimensional square Ising model with anisotropic nearest neighbour interaction.
|
PDF
1MB |
| Abstract: | An analytic expression for the phase boundary equation of the two-dimensional antiferromagnetic Ising square lattice with anisotropic nearest neighbour (Jx ̸= Jy) interactions under the influence of a constant external magnetic field (h) is derived using the domain wall method. The system undergoes an order-disorder phase transition at a critical temperature T = Tc that is given by the condition: e^ ((−2Jy+2h−4ph)/kbTc) (1 − e^(4Jx/kbTc)) = 1 + e^(4Jx/kbTc) + e^((2Jx+2h)/kbTc) + e^((2Jx−2h)/kbTc). The phase diagram for this condition is also derived. For vanishing magnetic field Onsager’s famous result, i.e. sinh(2Jx/kbTc) sinh(2Jy/kbTc) = 1 is recaptured. We also show that the domain wall method is exact and we conjecture that the entire system can be described by a domain wall of minimal length. |
| Item Type: | Essay (Bachelor) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics |
| Programme: | Applied Mathematics BSc (56965) |
| Link to this item: | https://purl.utwente.nl/essays/102327 |
| Export this item as: | BibTeX EndNote HTML Citation Reference Manager |
Show download statistics for this publication
Show download statistics for this publicationRepository Staff Only: item control page