We study globally bounded entire minimizers $u:\mathbb{ R}^n\rightarrow\mathbb{ R}^m$ of Allen-Cahn systems for potentials $W\geq 0$ with $\{ W=0\}=\{ a_1,...,a_N\}$ and $W(u)\sim |u-a_i|^\alpha$ near $u=a_i$, $0<\alpha<2$. Such solutions are, over large regions, identically equal to some zeroes of the potential $a_i$'s. We establish the estimates \begin{ equation*} \mathcal{ L}^n(I_0\cap B_r(x_0))\leq c_1r^{ n-1},\quad \mathcal{ H}^{ n-1}(\partial^* I_0\cap B_r(x_0))\geq c_2r^{ n-1}, \quad r\geq r_0(x_0) \end{ equation*} for the diffuse interface $I_0:=\{ x\in\mathbb{ R}^n: \min_{ 1\leq i\leq N}|u(x)-a_i|>0\}$ and the free boundary $\partial I_0$. Furthermore, if $\alpha=1$ we establish the upper bound \begin{ equation*} \mathcal{ H}^{ n-1}(\partial^* I_0\cap B_r(x_0))\leq c_3r^{ n-1}, \quad r\geq r_0(x_0). \end{ equation*}
Categories: math.AP