= Two-sublattice Ising variational free energy
{title2=$A=\frac{qJ}{2}M_BM_W-\frac h2(M_B+M_W)-\frac g2(M_B-M_W)+\frac{k_BT}{2}[s(M_B)+s(M_W)]$}
Here $s(m)=\frac{1+m}{2}\ln\frac{1+m}{2}+\frac{1-m}{2}\ln\frac{1-m}{2}$. This <free-energy density> is the <energy> minus temperature times <entropy> of independent sublattice <Ising spins>. Since $s'(m)=\operatorname{atanh}m$, stationarity yields the <two-sublattice Ising mean-field approximation>. Writing $M_\pm=(M_B\pm M_W)/2$, the quadratic coefficients are $(k_BT+qJ)/2$ for $M_+^2$ and $(k_BT-qJ)/2$ for $M_-^2$. The positive quartic coefficient $k_BT/12$ in the staggered direction stabilizes the continuous transition. Unlike a log-cosh auxiliary potential, this variational expression can be minimized away from self-consistency.
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