Comment on "Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions"

In a recent paper by Fronczak et al. [Phys. Rev. E 101, 022111 (2020)2470-004510.1103/PhysRevE.101.022111], a simple spin model has been studied in full detail via microcanonical approaches. The authors stress that the range of microcanonical temperature β_{m}>1 is unattainable in this model and the system undergoes a phase transition when the external parameter a=1 in the microcanonical ensemble. The purpose of this comment is to state that the treatment of the microcanonical entropy in the commented paper is inappropriate since the fact that ergodicity is broken in the microcanonical dynamics is ignored by the authors. The phase transition in the microcanonical ensemble, considered in the commented paper, could occur only with a nonlocal dynamics which is often difficult to justify physically.