  We investigate the Ising model in one, two, and three dimensions using a
cumulant method that allows us to determine the Lee-Yang zeros from the
magnetization fluctuations in small lattices. By doing so with increasing
system size, we are able to determine the convergence point of the Lee-Yang
zeros in the thermodynamic limit and thereby predict the occurrence of a phase
transition. The cumulant method is attractive from an experimental point of
view since it uses fluctuations of measurable quantities, such as the
magnetization in a spin lattice, and it can be applied to a variety of
equilibrium and non-equilibrium problems. We show that the Lee-Yang zeros
encode important information about the rare fluctuations of the magnetization.
Specifically, by using a simple ansatz for the free energy, we express the
large-deviation function of the magnetization in terms of Lee-Yang zeros. This
result may hold for many systems that exhibit a first-order phase transition.
