  Renewal processes generated by a power-law distribution of intervals with
tail index less than unity are genuinely non-stationary. This issue is
illustrated by a critical review of the recent paper by Barma, Majumdar and
Mukamel 2019 \textit{J.~Phys.~A} {\bf 52} 254001, devoted to the investigation
of the properties of a specific one-dimensional equilibrium spin system with
long-range interactions. We explain why discarding the non-stationarity of the
process underlying the model leads to an incorrect expression of the critical
spin-spin correlation function, even when the system, subjected to periodic
boundary conditions, is translation invariant.
