Moment-generating function zeros in the study of phase transitions

Partition function zeros play a central role in the study of phase transitions. Recently, energy probability distribution (EPD) zeros were proposed as an alternative approach that solves some of the implementation issues present in the Fisher zeros method by allowing drastic reduction of the polynomial. Here, a formulation based on the EPD zeros that can reduce even more the polynomial degree while maintaining its accuracy is presented. This method has shown to be computationally cheaper than the EPD zeros, allowing the study of systems by using partition function zeros that would be unfeasible otherwise. In addition, the method can be easily extended to study phase transitions in external fields while maintaining all of its improvements.