Probing criticality with linearly varying external fields: Renormalization group theory of nonequilibrium critical dynamics under driving

A renormalization group theory for the nonlinear and nonequilibrium responses to linearly varying external probes is formulated for the critical dynamics of a time-dependent Ginzburg-Landau equation with a scalar nonconserved order parameter. A series of nonequilibrium dynamic critical exponents and their scaling relations characterizing the time-dependent probes and the nonequilibrium hysteresis induced are derived analytically and systematically and agree well with numerical results. The three-dimensional dynamic critical exponent is accordingly determined as z = 2.036(11). These show that the linearly varying external fields can be applied to probe criticality effectively.