  The recent progress in the optimization of two-dimensional tensor networks
[H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X ${\bf 9}$, 031041
(2019)] based on automatic differentiation opened the way towards precise and
fast optimization of such states and, in particular, infinite projected
entangled-pair states (iPEPS) that constitute a generic-purpose ${\it Ansatz}$
for lattice problems governed by local Hamiltonians. In this work, we perform
an extensive study of a paradigmatic model of frustrated magnetism, the
$J_1-J_2$ Heisenberg antiferromagnet on the square lattice. By using advances
in both optimization and subsequent data analysis, through finite
correlation-length scaling, we report accurate estimations of the magnetization
curve in the N\'eel phase for $J_2/J_1 \le 0.45$. The unrestricted iPEPS
simulations reveal an $U(1)$ symmetric structure, which we identify and impose
on tensors, resulting in a clean and consistent picture of antiferromagnetic
order vanishing at the phase transition with a quantum paramagnet at $J_2/J_1
\approx 0.46(1)$. The present methodology can be extended beyond this model to
study generic order-to-disorder transitions in magnetic systems.
