Phase self-calibration (or selfcal) is an algorithm often used in the calibration of interferometric observations in astronomy. Although a powerful tool, this algorithm presents strong limitations when applied to data with a low signal-to-noise ratio. We analyze the artifacts that the phase selfcal algorithm produces when applied to extremely noisy data. We show how the phase selfcal may generate a spurious source in the sky from a distribution of completely random visibilities. This spurious source is indistinguishable from a real one. We numerically and analytically compute the relationship between the maximum spurious flux density generated by selfcal from noise and the particulars of the interferometric observations. Finally, we present two simple tests that can be applied to interferometric data for checking whether a source detection is real or whether the source is an artifact of the phase self-calibration algorithm.