On Huang page 417 he talks about Landau Theory and he says that in the neighborhood of a critical point where m(x) is small, we can expand the landau free energy


In powers of m(x) and it’s derivatives

$$\psi(m(x),H(x))= \frac{1}{2}|\nabla m(x)|^2-\frac{1}{KT}m(x)H(x)+\frac{1}{2}r_0m^2(x)+s_0m^3(x)+u_0m^4(x)$$

But I’m not seeing how this is the expansion. Why do we have a modulus squared in an expansion?

Similar Q: Differentiating Landau free energy functional from the energy levels of a system


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