Nonlinear relaxation near the critical point: Molecular-field and scaling theory

We examine the critical-point singularity of the nonlinear relaxation of purely dissipative systems. Applying the molecular-field approximation to the time-dependent Ginzburg-Landau model, it is shown that the critical exponent of the nonlinear relaxation time (${\Delta }^{\mathrm{}\left(\mathrm{nl}\right)\mathrm{}}$) can be different from that of the linear one (${\Delta }^{\mathrm{}\left(l\right)\mathrm{}}$) even in ergodic systems. From the assumptions that scaling applies and that only the near-equilibrium fluctuations significantly affect the relaxation time, a scaling law ${\Delta }^{\mathrm{}\left(\mathrm{nl}\right)\mathrm{}}={\Delta }^{\mathrm{}\left(l\right)\mathrm{}}-\beta$ is derived ($\beta$ is the critical exponent of the order). On the base of this scaling law we reanalyze the available Monte Carlo calculations, high-temperature series, and the critical-slowing-down experiment on ${\mathrm{Ni}}_3$Mn.