On the use of partition function zeros to study of phase transitions using computer simulationsLucas A.S. Mól, Universidade Federal de Minas Gerais, Brazil

In this talk, I will explore recent techniques for studying phase transitions using computer simulations with a focus on the use of complex zeros of the Energy Moment Generation Function. This approach allows one to approach the transition temperature at will, obtaining valuable information about the transition at a relatively low computational cost. This technique improves upon the Fisher zeros method by allowing one to extract partial information about the complex zero map by analyzing energy moments at specific temperatures, rather than relying on the full density of states required for the complete Fisher zero map. Furthermore, this formulation can be extended to study phase transitions driven by other fields by using the moments of quantities such as magnetization. I will discuss the connections and similarities between this method, the traditional Fisher zeros approach, and Cumulant-based techniques, while also addressing the limitations and challenges inherent to this framework. The combination of these methods with traditional approaches promises to deepen our understanding of phase transitions.