  We consider two-dimensional zero-temperature systems of $N$ particles to
which we associate an energy of the form $$ \mathcal{E}[V](X):=\sum_{1\le
i<j\le N}V(|X(i)-X(j)|), $$ where $X(j)\in\mathbb R^2$ represents the position
of the particle $j$ and $V(r)\in\mathbb R$ is the {pairwise interaction} energy
potential of two particles placed at distance $r$. We show that under suitable
assumptions on the single-well potential $V$, the ground state energy per
particle converges to an explicit constant $\bar{\mathcal E}_{\mathrm{sq}}[V]$
which is the same as the energy per particle in the square lattice infinite
configuration. We thus have $$ N{\bar{\mathcal E}_{\mathrm{sq}}[V]}\le
\min_{X:\{1,\ldots,N\}\to\mathbb R^2}\mathcal E[V](X)\le N{\bar{\mathcal
E}_{\mathrm{sq}}[V]}+O(N^{\frac 1 2}). $$ Moreover $\bar{\mathcal
E}_{\mathrm{sq}}[V]$ is also re-expressed as the minimizer of a four point
energy.
  In particular, this happen{s} if the potential $V$ is such that
$V(r)=+\infty$ for $r<1$, $V(r)=-1$ for $r\in [1,\sqrt{2}]$, $V(r)=0$ if
$r>\sqrt{2}$, in which case ${\bar{\mathcal E}_{\mathrm{sq}}[V]}=-4$.
  To the best of our knowledge, this is the first proof of crystallization to
the square lattice for a two-body interaction energy.
