Critical behavior of the driven Curie-Weiss model

We complete the phase diagram of the macroscopic Curie-Weiss magnet in a time-periodic external field, as a function of temperature and driving parameters. There is a regime (large enough driving amplitude and frequency, at low temperatures) where stable paramagnetic and ferromagnetic phases coexist. In particular, we present a new detailed analysis of the (nonequilibrium) specific heat, diverging at the same critical inverse temperature $\beta_c$ as the magnetic susceptibility. The new Curie temperature decreases with the driving, and we find critical exponent $\alpha=1$ for $\beta\downarrow \beta_c$, and $\alpha\simeq 0.86$ for $\beta\uparrow \beta_c$, even for small driving. A Floquet analysis shows the nature of the criticality, which is dynamical, with implications that remain unseen and are mostly impossible when the system is in thermal equilibrium.