The goal of this paper is to prove singularity of three natural fields in QFT with respect to their natural base measure. The fields we consider are the following ones: (1) The near-critical limit of the $2d$ Ising model (in the $β$-direction) is locally singular w.r.t the critical scaling limit of $2d$ Ising. (N.B. In the $h$-direction it is not locally singular). (2) The $2d$ Hierarchical Sine-Gordon field is singular w.r.t the $2d$ hierarchical Gaussian Free Field for all $β\in[β_{L^2}, β_{BKT})$. (3) The Hierarchical $Φ^4_3$ field is singular w.r.t the $3d$ hierarchical GFF. Item (1) gives the first strong indication that the energy field of critical $2d$ Ising model does not exist as a random Schwarz distribution on the plane. Item (2) has been proved to be singular for the non-hierarchical $2d$ Sine-Gordon sufficiently far from the BKT point in [GM24] while item (3) is proved to be singular for the non-hierarchical $3d$ $Φ^4_3$ field in [BG21, OOT21, HKN24]. We believe our way to detect a singular behaviour at all scales is very much down to earth and may be applicable in all settings where one has a good enough control on the so-called effective potentials.