The

Context. Recent spectroscopic surveys have begun to explore the Galactic disk system on the basis of large data samples, with spatial distributions sampling regions well outside the solar neighborhood. In this way, they provide valuable information for testing spatial and temporal variations of disk structure kinematics and chemical evolution. Aims. The main purposes of this study are to demonstrate the usefulness of a rigorous mathematical approach to separate substructures of a stellar sample in the abundance-metallicity plane, and provide new evidence with which to characterize the nature of the metal-poor end of the thin disk sequence. Methods. We used a Gaussian mixture model algorithm to separate in the [Mg/Fe] vs. [Fe/H] plane a clean disk star subsample (essentially at RGC< 10 kpc) from the Gaia-ESO survey (GES) internal data release 2 (iDR2). We aim at decomposing it into data groups highlighting number density and/or slope variations in the abundance-metallicity plane. An independent sample of disk red clump stars from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) was used to cross-check the identified features. Results. We find that the sample is separated into five groups associated with major Galactic components; the metal-rich end of the halo, the thick disk, and three subgroups for the thin disk sequence. This is confirmed with the sample of red clump stars from APOGEE. The three thin disk groups served to explore this sequence in more detail. The two metal-intermediate and metal-rich groups of the thin disk decomposition ([Fe/H] > −0.25 dex) highlight a change in the slope at solar metallicity. This holds true at different radial regions of the Milky Way. The distribution of Galactocentric radial distances of the metal-poor part of the thin disk ([Fe/H] < −0.25 dex) is shifted to larger distances than those of the more metal-rich parts. Moreover, the metal-poor part of the thin disk presents indications of a scale height intermediate between those of the thick and the rest of the thin disk, and it displays higher azimuthal velocities than the latter. These stars might have formed and evolved in parallel and/or dissociated from the inside-out formation taking place in the internal thin disk. Their enhancement levels might be due to their origin from gas pre-enriched by outflows from the thick disk or the inner halo. The smooth trends of their properties (their spatial distribution with respect to the plane, in particular) with [Fe/H] and [Mg/Fe] suggested by the data indicates a quiet dynamical evolution, with no relevant merger events