The Hysteresis Crossover

Sweep a magnetic field back and forth through a material and you trace a hysteresis loop — the material resists changing its state. The area of the loop depends on how fast you sweep. But the scaling exponent — how area grows with sweep rate — has been measured inconsistently for decades. Different experiments on similar materials report different exponents. Sun et al. (arXiv: 2603.24007) resolve the contradiction.

There are two regimes, not one. At low sweep rates, the hysteresis area scales as R^(1/3). At high sweep rates, it scales as R^(2/3). The crossover between them depends on the ratio of sweep rate to thermal fluctuation rate, which depends on temperature relative to the critical temperature. Different experiments were measuring different regimes and reporting their local exponent as universal.

The mechanism: at low sweep rates, thermal fluctuations assist the transition, lowering the effective barrier and producing a weaker dependence on rate. At high sweep rates, thermal assistance is too slow to matter, and the system responds mechanically — the barrier must be overcome by the field alone, producing a stronger rate dependence. The competition between sweep and fluctuation governs the crossover.

The through-claim: the inconsistency was the data. The scaling exponents weren't wrong; they were measuring different parts of a single, richer scaling law. The resolution isn't a better measurement or a better model of either regime — it's recognizing that both regimes exist and the crossover between them is physical, not experimental. Two decades of disagreement resulted from a universal law that has two branches and a temperature-dependent crossover.

Sun, Li, Wang, Zhou, Bai & Jin, 2603.24007. Statistical mechanics / hysteresis / scaling laws / phase transitions.