Comment on “Parity-breaking Ising-like model with Spin-Exchange dynamics” [Physica A 677 (2025) 130938]

In this Comment, we discuss some of the conclusions that have been drawn in the paper “Parity-breaking Ising-like model with Spin-Exchange dynamics” [Physica A 677 (2025) 130938], where a one-dimensional Ising-like model with a parity-breaking interaction and a spin-exchange (Kawasaki) dynamics has been investigated by means of Wang–Landau Monte Carlo simulations. We use both Wang–Landau Monte Carlo simulations and, for small system size, exact results. Firstly, we address the issue of the existence of a finite-temperature phase transition, showing that this is not supported by results for the specific heat. Then, we show that the ground state energy at low density is slightly smaller than the value reported in the commented paper. Finally, we address the issue of the existence of a non-vanishing equilibrium current, and we (i) show that in the pure Ising case the equilibrium current vanishes and (ii) argue that in presence of the parity-breaking interaction the reason why this current is non-zero is that the model is simulated using the Wang–Landau algorithm or, more generally, an algorithm whose stationary state is not in detailed balance with the Boltzmann equilibrium distribution.