Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic “bias” field, H_b, for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, δ_d, of H_b at the critical period of the DPT is equal to the exponent for the critical isotherm, δ_e, in the equilibrium Ising model. This implies that H_b is a significant component of the field conjugate to Q. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of H_b in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature T_eff(T,P,H₀) depending on the period, and possibly the temperature and field amplitude, holds for the variables Q and H_b. This FDR justifies the use of the scaled variance of Q as a proxy for the nonequilibrium susceptibility, ∂⟨Q⟩∕∂H_b, in the critical region.