Hysteresis scaling of the field-driven first-order phase transition in the Ising model

Dynamical phase transitions in the Ising model on hypercubic lattices are considered. Under a linearly swept magnetic field, the hysteresis loop that characterizes the held-driven first-order phase transition is studied carefully. Using the Glauber dynamics, we find that, in the mean-field approximation, the energy dissipation of this phase transition or the hysteresis loop area A of the M-H curve can be scaled with respect to the sweep rate h of magnetic field in the form A - A(0) proportional to h(b), A(0) proportional to (T-c -T)(a) with a = 2 and b = 2/3. However, b varies (b < 2/3) when fluctuations and spin correlations are taken into account. Monte Carlo simulation is used to obtain the scaling relation for A in two-, three-and four-dimensionalIsing models and we obtain the exponents b = 0.36 +/- 0.06, 0.52 +/- 0.04 and 0.65 +/- 0.04 respectively. These exponents are obviously different from those obtained by scaling A as A proportional to h(b)T(-c) for any temperatures in Ising models under a sinusoidal field. Finally we point out that, in the concept of universality, field-driven first-order phase transitions in the Ising model in different dimensions belong to different universal classes due to the spin fluctuation and correlation below the Curie temperature.