  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*}
