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This paper explores the use of a cumulant method to determine the zeros ofpartition functions for continuous phase transitions. Unlike a first-ordertransition, with a uniform density of zeros near the transition point, acontinuous transition is expected to show a power law dependence of the densitywith a nontrivial slope for the line of zeros. Different types of models andmethods 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 simulationsfor the well-known square lattice Ising model. The method is applicable forclosest zeros near the imaginary axis, as these are needed for dynamicalquantum phase transitions. In all cases, the method is found to provide thebasic information about the transition, and most importantly, avoids rootfinding methods.

Zeros of partition function for Continuous Phase Transitions using cumulants