We investigate the Dyson-Schwinger equations for the gluon and ghost
propagators and the ghost-gluon vertex of Landau-gauge gluodynamics in two
dimensions. While this simplifies some aspects of the calculations as compared
to three and four dimensions, new complications arise due to a mixing of
different momentum regimes. As a result, the solutions for the propagators are
more sensitive to changes in the three-point functions and the ansaetze used
for them at the leading order in a vertex a expansion. Here, we therefore go
beyond this common truncation by including the ghost-gluon vertex
self-consistently for the first time, while using a model for the three-gluon
vertex which reproduces the known infrared asymptotics and the zeros at
intermediate momenta as observed on the lattice. A separate computation of the
three-gluon vertex from the results is used to confirm the stability of this
behavior a posteriori. We also present further arguments for the absence of the
decoupling solution in two dimensions. Finally, we show how in general the
infrared exponent kappa of the scaling solutions in two, three and four
dimensions can be changed by allowing an angle dependence and thus an essential
singularity of the ghost-gluon vertex in the infrared.Comment: 24 pages; added references, improved choices of parameters for vertex
models; identical to version published in JHE
