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We establish the energy minimality property of solutions to the generalizedPainlev\'{e}-II equation $\Delta y-x_1y-2y^3=0$, $(x_1,x_2)\in \mathbb{R}^2$,which are increasing in $x_2$ and converge to the positive and negativeHastings-McLeod solutions as $x_2\to \pm \infty$.

Energy minimality property of the connecting solution of the Painlev\'{e} phase transition model