# Zeros of partition function for Continuous Phase Transitions using cumulants

## TL;DR

This paper introduces a cumulant-based method to identify zeros of partition functions in continuous phase transitions, providing insights into transition properties without requiring root-finding algorithms.

## Contribution

The paper presents a novel cumulant approach to determine partition function zeros for continuous phase transitions, applicable across various models and avoiding root-finding procedures.

## Key findings

- Method accurately identifies zeros near the imaginary axis.
- Applicable to diverse models including DNA melting and Ising model.
- Provides key transition information without root finding.

## Abstract

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.