  Lee-Yang zeros are points in the complex plane of an external control
parameter at which the partition function vanishes for a many-body system of
finite size. In the thermodynamic limit, the Lee-Yang zeros approach the
critical value on the real-axis, where a phase transition occurs. Partition
function zeros have for many years been considered a purely theoretical
concept, however, the situation is changing now as Lee-Yang zeros have been
determined in several recent experiments. Motivated by these developments, we
here devise a direct pathway from measurements of partition function zeros to
the determination of critical points and universal critical exponents of
continuous phase transitions. To illustrate the feasibility of our approach, we
extract the critical exponents of the Ising model in two and three dimensions
from the fluctuations of the total energy and the magnetization in lattices of
finite size. Importantly, the critical exponents can be determined even if the
system is away from the phase transition. Moreover, in contrast to standard
methods based on Binder cumulants, it is not necessary to drive the system
across the phase transition. As such, our method provides an intriguing
perspective for investigations of phase transitions that may be hard to reach
experimentally, for instance at very low temperatures or at very high
pressures.
