Dynamic hysteresis at a noisy saddle-node shows power-law scaling but nonuniversal exponent

Dynamic hysteresis, viz., delay in switching of a bistable system on account of the finite sweep rate of the drive has been extensively studied in dynamical and thermodynamic systems. Dynamic hysteresis results from slowing of the response around a saddle-node bifurcation. As a consequence, the hysteresis area increases with the sweep rate. Mean-field theory, relevant for noise-free situations, predicts power law scaling with the area scaling exponent of 2/3. We have experimentally investigated the dynamic hysteresis for a thermally-driven metal-insulator transition in a high quality NdNiO$_3$ thin film and found the scaling exponent to be about 1/3, far less than the mean field value. To understand this, we have numerically studied Langevin dynamics of the order parameter and found that noise, which can be thought to parallel finite temperature effects, influences the character of dynamic hysteresis by systematically lowering the dynamical exponent to as small as 0.2. The power law scaling character, on the other hand, is unaffected in the range of chosen parameters. This work rationalizes the ubiquitous power law scaling of the dynamic hysteresis as well as the wide variation in the scaling exponent between 0.66 and 0.2 observed in different systems over the last 30 years.