Cumulants in the 3-dimensional Ising, O(2) and O(4) spin models

TL;DR

This paper investigates the critical behavior of cumulants and their ratios in 3D Ising, O(2), and O(4) spin models, revealing sign changes near critical temperatures and consistent qualitative patterns across models.

Contribution

It demonstrates the universal critical behavior of cumulants in different spin models relevant to QCD phase transitions, highlighting sign changes and qualitative similarities.

Findings

Higher cumulant ratios change sign near critical temperature.

Qualitative critical behavior is consistent across models.

Results support universality in phase transition characteristics.

Abstract

Based on the universal properties of a critical point in different systems and that the QCD phase transitions fall into the same universality classes as the 3-dimensional Ising, $O(2)$ or $O(4)$ spin models, the critical behavior of cumulants and higher cumulant ratios of the order parameter from the three kinds of spin models is studied. We found that all higher cumulant ratios change dramatically the sign near the critical temperature. The qualitative critical behavior of the same order cumulant ratio is consistent in these three models.