  We compute the topological susceptibility slope $\chi^\prime$, related to the
second moment of the two-point correlator of the topological charge density, of
$2d$ $\mathrm{CP}^{N-1}$ models for $N=5,11,21$ and $31$ from lattice Monte
Carlo simulations. Our strategy consists in performing a double limit: first,
we take the continuum limit of $\chi^\prime$ at fixed smoothing radius in
physical units; then, we take the zero-smoothing-radius limit. Since the same
strategy can also be applied to $4d$ gauge theories and full QCD, where
$\chi^\prime$ plays an intriguing theoretical and phenomenological role, this
work constitutes a step towards the lattice investigation of this quantity in
such models.
