# Condensation of Lee-Yang zeros in scalar field theory

## TL;DR

This paper demonstrates how Lee-Yang zeros in scalar field theories condense at the critical point, revealing fractal structures and scaling laws that could inform finite-size scaling in QCD near criticality.

## Contribution

It establishes a connection between Lee-Yang zeros and critical phenomena in scalar field theories, highlighting their role in finite-size scaling and potential applications to QCD.

## Key findings

- Zeros condense at the critical point as system size increases
- Zeros form a fractal structure influencing critical behavior
- Scaling laws relate zero distribution to critical exponents

## Abstract

We show that, at the critical temperature, there is a class of Lee-Yang zeros of the partition function in a general scalar field theory, which location scales with the size of the system with a characteristic exponent expressed in terms of the isothermal critical exponent $\delta$. In the thermodynamic limit the zeros belonging to this class condense to the critical point {\zeta}=1 on the real axis in the complex fugacity plane while the complementary set of zeros (with Re {\zeta} < 1) covers uniformly the unit circle. Although the aforementioned class degenerates to a single point for an infinite system, when the size is finite it dominates in the partition function and determines the self-similar structure (fractal geometry, scaling laws) of the critical system. This property opens up the perspective to formulate finite-size scaling theory in effective QCD, near the chiral critical point, in terms of the location of Lee-Yang zeros.