Dynamic scaling of hysteresis in a linearly driven system

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Abstract
We investigate the scaling behaviour of hysteresis in three-dimensional continuum models in a linear driving mode. A non-conserving N-component vector Phi is the order parameter and its dynamics are specified by the time-dependent Ginzburg-Landau theory. The ( Phi 2)2 and ( Phi 2)3 models embody spatial fluctuations of Phi and their free-energy functionals have a ( Phi 2)2 and a ( Phi 2)3 interaction, respectively, with O(N) symmetry. On the other hand, the mean-field model ignores all spatial fluctuations of Phi . The area A of hysteresis loop, the energy dissipation per cycle, is taken as functions of the scanning rate R and temperature. For the ferromagnetic first-order phase transition (FOPT), a scaling relation A=aRn is determined where R is the field-sweeping rate, a is the coefficient and the exponent n approximately= 1/2 . We also discuss experimental evidence for real systems compatible with this result, which shows that the driving rate dependence of energy dissipation is important in non-equilibrium FOPT.