= Critical point of an energy functional
{title2=$\delta E=0$}
= Stationary field configuration
{synonym}
A field configuration is critical for an <energy functional> $E$ if its <first variation> vanishes for every admissible infinitesimal field variation. For $E[\phi]=\int(\tfrac12|\nabla\phi|^2+U(\phi))$, integration by parts against compactly supported variations gives $\delta E=\int(-\Delta\phi+U'(\phi))\delta\phi$, so <stationary field configurations> satisfy the <Euler-Lagrange equation> $\Delta\phi=U'(\phi)$. A constrained target instead allows only tangent variations, changing that field equation. Criticality is stationarity, not necessarily energetic stability or a local minimum.
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