Effective Polyakov Loop Dynamics for Finite Temperature G(2) Gluodynamics

TL;DR

This paper develops effective 3D models for Polyakov loops in finite-temperature G_2 gluodynamics using strong coupling expansion, mean field approximation, and Monte Carlo simulations, revealing complex phase structures and transitions.

Contribution

It introduces both continuous and discrete effective models for G_2 gluodynamics, connecting them with phase transition behavior and validating predictions with simulations.

Findings

Rich phase diagram with multiple phases and transition types

Mean field predictions align well with Monte Carlo results

Discrete spin model captures key phase structure features

Abstract

Based on the strong coupling expansion we obtain effective 3-dimensional models for the Polyakov loop in finite-temperature G_2 gluodynamics. The Svetitsky-Jaffe conjecture relates the resulting continuous spin models with G_2 gluodynamics near phase transition points. In the present work we analyse the effective theory in leading order with the help of a generalised mean field approximation and with detailed Monte-Carlo simulations. In addition we derive a Potts-type discrete spin model by restricting the characters of the Polyakov loops to the three extremal points of the fundamental domain of G_2. Both the continuous and discrete effective models show a rich phase structure with a ferromagnetic, symmetric and several anti-ferromagnetic phases. The phase diagram contains first and second order transition lines and tricritical points. The modified mean field predictions compare very well with the results of our simulations.