  This paper explores the use of a cumulant method to determine the zeros of
partition functions for continuous phase transitions. Unlike a first-order
transition, with a uniform density of zeros near the transition point, a
continuous transition is expected to show a power law dependence of the density
with a nontrivial slope for the line of zeros. Different types of models and
methods of generating cumulants are used as a testing ground for the method.
These include exactly solvable DNA melting problem on hierarchical lattices,
heterogeneous DNA melting with randomness in sequence, Monte Carlo simulations
for the well-known square lattice Ising model. The method is applicable for
closest zeros near the imaginary axis, as these are needed for dynamical
quantum phase transitions. In all cases, the method is found to provide the
basic information about the transition, and most importantly, avoids root
finding methods.
