# Determination of universal critical exponents using Lee-Yang theory

## TL;DR

This paper introduces a novel method to determine universal critical exponents from measurements of Lee-Yang zeros, enabling analysis of phase transitions without crossing the critical point, applicable even in challenging experimental conditions.

## Contribution

The authors develop a direct approach linking partition function zeros to critical exponents, demonstrated on the 2D and 3D Ising models, bypassing traditional crossing methods.

## Key findings

- Critical exponents can be extracted from energy and magnetization fluctuations.
- Method works even when system is away from the phase transition.
- No need to drive the system across the phase transition.

## Abstract

Lee-Yang zeros are points in the complex plane of an external control parameter at which the partition function vanishes for a many-body system of finite size. In the thermodynamic limit, the Lee-Yang zeros approach the critical value on the real-axis, where a phase transition occurs. Partition function zeros have for many years been considered a purely theoretical concept, however, the situation is changing now as Lee-Yang zeros have been determined in several recent experiments. Motivated by these developments, we here devise a direct pathway from measurements of partition function zeros to the determination of critical points and universal critical exponents of continuous phase transitions. To illustrate the feasibility of our approach, we extract the critical exponents of the Ising model in two and three dimensions from the fluctuations of the total energy and the magnetization in lattices of finite size. Importantly, the critical exponents can be determined even if the system is away from the phase transition. Moreover, in contrast to standard methods based on Binder cumulants, it is not necessary to drive the system across the phase transition. As such, our method provides an intriguing perspective for investigations of phase transitions that may be hard to reach experimentally, for instance at very low temperatures or at very high pressures.