  We investigate the Allen-Cahn system
  \begin{equation*}
  \Delta u-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2,
  \end{equation*}
  where $W\in C^2(\mathbb{R}^2,[0,+\infty))$ is a potential with three global
minima. We establish the existence of an entire solution $u$ which possesses a
triple junction structure. The main strategy is to study the global minimizer
$u_\varepsilon$ of the variational problem
  \begin{equation*}
  \min\int_{B_1} \left( \frac{\varepsilon}{2}|\nabla
u|^2+\frac{1}{\varepsilon}W(u) \right)\,dz,\ \ u=g_\varepsilon \text{ on
}\partial B_1.
  \end{equation*}
  The point of departure is an energy lower bound that plays a crucial role in
estimating the location and size of the diffuse interface. We do not impose any
symmetry hypothesis on the solution.
