= Solution
An <order parameter> distinguishes phases by an equilibrium expectation value. For an <Ising model>, the local field $M(x)$ is the coarse-grained <magnetization>, and the uniform value is $M=N^{-1}\langle\sum_r\sigma_r\rangle$. The <spin inversion symmetry> maps $M$ to $-M$, so at zero field the <Landau free energy> contains even powers. Its disordered minimum is $M=0$; ordered <pure thermodynamic phases> have $M=\pm M_0$. Their sign is selected by taking the <thermodynamic limit> before sending $h$ to zero. A symmetric mixture can have zero average without being a single disordered phase. The term $-hM$ identifies $h$ as the <field conjugate to an order parameter>.
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