5 Dynamic Phase Diagram for a Periodically Driven Kinetic Square-lattice Ising Ferromagnet: Finite-size Scaling Evidence for the Absence of a Tri-critical Point

We discuss the subtle finite-size effects of the dynamic phase transition (DPT) in a two-dimensional kinetic Ising ferromagnet driven by an oscillating external field. We present computational and analytical evidence that there is no finite-temperature tri-critical point in the dynamic phase diagram of this model. This contrasts with earlier claims [1–3] for the existence of a tri-critical point in this model. Careful finite-size scaling analysis of Monte Carlo simulations reveals that the negative dip of the Binder cumulant and the corresponding multi-peak orderparameter distribution (often characteristic of a first-order transition) are merely finite-size effects in this case. When the DPT prevails in the infinite-system limit, it is always continuous. The misleading finite-size effects are related to the stochastic nature of the underlying metastable decay for “small” systems, which exhibit stochastic resonance.