= Solution
In <Landau-Ginzburg theory>, a scalar <order parameter> $M$ distinguishes macroscopic phases: for an <Ising model> it is the <magnetization> per site, while near a liquid–gas endpoint it can be a shifted density. An ordered <pure thermodynamic phase> has a nonzero value even when the conjugate field is removed. For a symmetry-related pair, take the <thermodynamic limit> before $h\to0^\pm$; a finite-volume symmetric ensemble instead has zero average.
Coarse-grain to a slowly varying real field and use a local, symmetry-constrained <free-energy density>. A useful convention is
$$
\mathcal F[M]=\int d^Dx\left[\frac K2(\nabla M)^2+\frac r2M^2+\frac u4M^4+\frac v6M^6-hM\right],\qquad K>0.
$$
For <spin inversion symmetry>, odd powers other than the externally imposed source are absent. Take $v>0$ when the quartic coefficient can be negative; for an ordinary transition $u>0$ already stabilizes the quartic truncation. The <gradient energy> penalizes spatial variations. In the <Landau approximation>, minimize this functional, usually first over constant fields. The corresponding <statistical field theory> also integrates fluctuations with weight $e^{-\mathcal F/(k_BT)}$. \b[The <order parameter> identifies the phase; its spatial field describes both equilibrium order and its fluctuations.]
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