Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 303 / 1 / a / iii

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- Solution iii

Solution

The Landau-Ginzburg theory promotes the order parameter to a field and penalizes spatial gradients:

F [m] = \int d^{d} x [\frac{κ}{2} ∣\nabla m ∣^{2} + α_{2} (T) m^{2} + α_{2 n} m^{2 n} - hm],

κ > 0

. Further even powers and higher-derivative terms may be included when required by accuracy.

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