  Detailed theoretical study of the magneto-optical properties of weakly
confining GaAs/AlGaAs quantum dots is provided. We focus on the diamagnetic
coefficient and the $g$-factor of the neutral and the charged excitonic states,
respectively, and their evolution with various dot sizes for the magnetic
fields applied along $[001]$ direction. For the calculations we utilize the
combination of ${\bf k}\cdot{\bf p}$ and the configuration interaction methods.
We decompose the theory into four levels of precision,~i.e., (i)
single-particle electron and hole states, (ii) non-interacting electron-hole
pair, (iii) electron-hole pair constructed from the ground state of both
quasiparticles and interacting via the Coulomb interaction (i.e. with minimal
amount of correlation), and (iv) that including the effect of correlation. The
aforementioned approach allows us to pinpoint the dominant influence of various
single- and multi-particle effects on the studied magneto-optical properties,
allowing the characterization of experiments using models which are as simple
as possible, yet retaining the detailed physical picture.
