Evolution of relevant parameters for bar formation. From top to bottom, the ELN criterion (Eq. (2)), MMW criterion (Eq. (3)), and Toomre parameter (Eq. (1)) for different galactic wind models (top figure) and BH physics models (bottom figure) and the original TNG50 are shown. Horizontal dashed lines represent the threshold that defines if a disc is unstable, and magenta shaded region represents the values where the disc is unstable. Thinner lines correspond to the evolution of each halo. Vertical solid lines and shaded region represent the median redshift and the distribution between 20^th and 80^th percentiles of the bar formation time. For TNG50-like, MW and SW models, the three instability criteria determine if a bar forms or not. For NW model, ELN and MMW criteria fail to predict a stable disc, whereas Toomre criterion fails to predict bar formation for WW model.