  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.
