= Solution
The single-spin average in the effective field is $\tanh(\beta B_{\rm eff})$. Requiring it to equal the assumed average gives the <mean-field self-consistency equation>
$$
\boxed{m=\tanh[\beta(B+2DJm)].}
$$
At $B=0$, the slope of its right side at the origin is $2DJ/(k_BT)$. Thus $\boxed{T_c=2DJ/k_B}$. For $T>T_c$, $m=0$ is the only solution and is the stable minimum: thermal fluctuations dominate. For $T<T_c$, two stable nonzero solutions $\pm m(T)$ represent <spontaneous magnetization>, while the zero solution is unstable. At $T_c$ they merge continuously. Expanding $\tanh x=x-x^3/3+\cdots$ near the transition yields $m^2\sim3(T_c-T)/T_c$, so the mean-field <critical exponent> is one-half. These are predictions of the approximation, not a proof of the exact Ising transition in every dimension.
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