Yang-Lee zeros for real-space condensation

TL;DR

This paper derives an exact formula for the distribution of Yang-Lee zeros in a model exhibiting real-space condensation, revealing how phase transitions are reflected in zero distributions and providing insights into critical phenomena.

Contribution

It introduces an exact solution for Yang-Lee zeros in a general weighted random allocation model, linking zero distribution to phase transitions and critical behavior.

Findings

Zeros form a conformal mapping of uniform phases

Zero density scaling at critical point is characterized

Model allows tuning of phase transition order and exponents

Abstract

Using the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero distribution in the random allocation model of general weights. This exhibits a real-space condensation phase transition, which is induced by a pressure change. The exact solution allows one to read off the scaling of the density of zeros at the critical point and the angle at which locus of zeros hits the critical point. Since the order of the phase transition and critical exponents can be tuned with a single parameter for several families of weights, the model provides a useful testing ground for verifying various relations between the distribution of zeros and the critical behavior, as well as for exploring the behavior of physical quantities in the mesoscopic regime, i.e., systems of large but finite size. The main result is that asymptotically the Yang-Lee zeros are images of a conformal mapping, given by the generating function for the weights, of uniformly distributed complex phases.