Partition function zeros of zeta-urns

TL;DR

This paper analyzes the distribution of partition function zeros in the zeta-urn model, revealing how these zeros behave near phase transitions and testing theoretical scaling predictions for different transition orders.

Contribution

It provides the first detailed computation of zeros' loci for finite-size zeta-urn systems and compares their scaling behavior with theoretical models for phase transitions.

Findings

Zeros accumulate near critical points as system size increases

Scaling relations match theoretical predictions for both first and higher order transitions

Distribution patterns of zeros differ between transition types

Abstract

We discuss the distribution of partition function zeros for the grand-canonical ensemble of the zeta-urn model, where tuning a single parameter can give a first or any higher order condensation transition. We compute the locus of zeros for finite-size systems and test scaling relations describing the accumulation of zeros near the critical point against theoretical predictions for both the first and higher order transition regimes.