  The Olbertian partition function is reformulated in terms of continuous
(Abelian) fields described by the Landau-Ginzburg action, respectively
Hamiltonian. In order do make some progress, the Gaussian approximation to the
partition function is transformed into the Olbertian prior to adding the
quartic Landau-Ginzburg term in the Hamiltonian. The final result is provided
in the form of an expansion suitable for application of diagrammatic techniques
once the nature of the field is given, i.e. once the field equations are
written down such that the interactions can be formulated.
