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

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.