Inverse Monte-Carlo and Demon Methods for Effective Polyakov Loop Models of SU(N)-YM

TL;DR

This paper develops and compares inverse Monte-Carlo and demon methods to construct effective Polyakov loop models for SU(N) Yang-Mills theories, capturing phase structures and analyzing phase transitions at finite temperature.

Contribution

It introduces an effective modeling approach for SU(N) YM theories using inverse Monte-Carlo and demon methods, including applications to SU(3) and SU(4) phase transitions.

Findings

Successful reproduction of phase structure including center and anti-center phases

Comparison of demon method with Schwinger-Dyson equations for coupling extraction

Application of canonical demon method to SU(4) phase transition

Abstract

We study effective Polyakov loop models for SU(N) Yang-Mills theories at finite temperature. In particular effective models for SU(3) YM with an additional adjoint Polyakov loop potential are considered. The rich phase structure including a center and anti-center directed phase is reproduced with an effective model utilizing the inverse Monte-Carlo method. The demon method as a possibility to obtain the effective models' couplings is compared to the method of Schwinger-Dyson equations. Thermalization effects of microcanonical and canonical demon method are analyzed. Finally the elaborate canonical demon method is applied to the finite temperature SU(4) YM phase transition.