Effective Polyakov loop dynamics for finite temperatureG2gluodynamics

Abstract

Based on the strong coupling expansion we obtain effective three-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 analyze the effective theory in leading order with the help of a generalized 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 antiferromagnetic 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.