High cumulants from the 3-dimensional $O(1, 2, 4)$ spin models

TL;DR

This paper uses Monte Carlo simulations of 3D O(1, 2, 4) spin models to analyze high cumulants of order parameters and energies, providing insights relevant to QCD phase transitions.

Contribution

It introduces detailed high cumulant calculations for different O(N) models, linking spin model results to QCD phase transition phenomena.

Findings

High cumulants of the order parameter and energy are computed for O(1) models.

Critical features of cumulants are identified and discussed.

Results are instructive for understanding net baryon number cumulants in QCD.

Abstract

Considering different universality classes of the QCD phase transitions, we perform the Monte Carlo simulations of the 3-dimensional $O(1, 2, 4)$ models at vanishing and non-vanishing external field, respectively. Interesting high cumulants of the order parameter and energy from O(1) (Ising) spin model, and the cumulants of the energy from O(2) and O(4) spin models are presented. The critical features of the cumulants are discussed. They are instructive to the high cumulants of the net baryon number in the QCD phase transitions.