  Spin models are the prime example of simplified manybody Hamiltonians used to
model complex, real-world strongly correlated materials. However, despite their
simplified character, their dynamics often cannot be simulated exactly on
classical computers as soon as the number of particles exceeds a few tens. For
this reason, the quantum simulation of spin Hamiltonians using the tools of
atomic and molecular physics has become very active over the last years, using
ultracold atoms or molecules in optical lattices, or trapped ions. All of these
approaches have their own assets, but also limitations. Here, we report on a
novel platform for the study of spin systems, using individual atoms trapped in
two-dimensional arrays of optical microtraps with arbitrary geometries, where
filling fractions range from 60 to 100% with exact knowledge of the initial
configuration. When excited to Rydberg D-states, the atoms undergo strong
interactions whose anisotropic character opens exciting prospects for
simulating exotic matter. We illustrate the versatility of our system by
studying the dynamics of an Ising-like spin-1/2 system in a transverse field
with up to thirty spins, for a variety of geometries in one and two dimensions,
and for a wide range of interaction strengths. For geometries where the
anisotropy is expected to have small effects we find an excellent agreement
with ab-initio simulations of the spin-1/2 system, while for strongly
anisotropic situations the multilevel structure of the D-states has a
measurable influence. Our findings establish arrays of single Rydberg atoms as
a versatile platform for the study of quantum magnetism.
