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The current associated with electric polarization and magnetization in matter. If the magnetic response is neglected, it is ${\mathbf{J}}_b={\partial }_t\mathbf{P}$. It is distinguished from a free conduction current in the Maxwell equations in matter.

The equilibrium magnetization is a value of the magnetization that minimizes the Landau free energy. A stable equilibrium has nonnegative second derivative with respect to the magnetization; degenerate nonzero minima describe symmetry-related magnetized phases.

The vacuum of the diagonal Bogoliubov quasiparticles has the displayed energy. In the thermodynamic bulk, $E_0/N=-J(2\pi {)}^{-1}{\int }_{-\pi }^{\pi }\sqrt{1+g^2-2g\cos k}dk$. The Hellmann–Feynman theorem then gives the field magnetization ${\sum }_n⟨S_n^z⟩={\sum }_{k}J(g-\cos k)/{ϵ}_k$. Sector-dependent finite-chain boundary terms must be restored when exact finite-size levels are needed.

The uniform mode of a pure Gaussian field theory with negative squared mass has an unbounded quadratic energy. Its partition function diverges even with a finite-volume ultraviolet regulator, so it supplies no stable ordered branch. At positive squared mass the zero-source average is zero. Thus the scaling dimension of the field can yield a formal order-parameter critical exponent without establishing a negative-reduced-temperature magnetization law. A stabilizing quartic interaction is relevant below four dimensions and ordinarily changes the critical theory to the Wilson-Fisher fixed point; above four its coefficient is a dangerously irrelevant coupling for the ordered phase.