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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.

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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:TNW: Science and Technology
Subject:33 physics
Programme:Applied Physics BSc (56962)
Link to this item:https://purl.utwente.nl/essays/100595
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