Critical heat current fluctuations in Curie-Weiss model in and out of equilibrium

In some models of nonequilibrium phase transitions, fluctuations of the analyzed currents have been observed to diverge with system size. To assess whether this behavior is universal across phase transitions, we examined heat current fluctuations in the Curie-Weiss model, a paradigmatic model of the paramagnetic-ferromagnetic phase transition, coupled to two thermal baths. This model exhibits phase transitions driven by both the temperature and the magnetic field. We find that at the temperature-driven phase transition, the heat current noise consists of two contributions: the equilibrium part, which vanishes with system size, and the nonequilibrium part, which diverges with system size. For small temperature differences, this leads to nonmonotonic scaling of fluctuations with system size. In contrast, at the magnetic-field-driven phase transition, heat current fluctuations do not diverge when observed precisely at the phase transition point. Instead, out of equilibrium, the noise is enhanced at the magnetic field values away but close to the phase transition point, due to stochastic switching between two current values. The maximum value of noise increases exponentially with system size, while the position of this maximum shifts towards the phase transition point. Finally, on the methodological side, the paper demonstrates that current fluctuations in large systems can be effectively characterized by combining a path-integral approach for macroscopic fluctuations together with an effective two-state model describing subextensive transitions between the two macroscopic states involved in the phase transition.