= Landau theory
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Landau theory describes phases using a symmetry-constrained expansion of an effective <free energy> in an <order parameter>. For a uniform scalar order parameter with sign-reversal symmetry, a simple example is
$$
f(m)=\frac a2m^2+\frac b4m^4-hm,\qquad b>0.
$$
At zero conjugate field $h$, positive $a$ favors $m=0$, while negative $a$ produces minima $m=\pm\sqrt{-a/b}$. The change in the minimum gives a simple model of continuous ordering.
The coefficients summarize microscopic effects rather than following from symmetry alone. A negative quartic coefficient requires stabilizing higher powers and can permit a first-order transition. Minimizing the expansion gives <mean-field critical exponents>; sufficiently strong fluctuations invalidate that approximation near criticality. <Landau-Ginzburg theory> introduces spatial gradients so the same framework can describe interfaces and correlations.
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