  We control quantum fluctuations to create the ground state magnetic phases of
a classical Ising model with a tunable longitudinal magnetic field using a
system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions,
the various ground state spin configurations are separated by multiple
first-order phase transitions, which in our zero temperature system cannot be
driven by thermal fluctuations. We instead use a transverse magnetic field as a
quantum catalyst to observe the first steps of the complete fractal devil's
staircase, which emerges in the thermodynamic limit and can be mapped to a
large number of many-body and energy-optimization problems.
