Nonlinear-response theory of Ising-like systems

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Abstract
The nonequilibrium response of a two-dimensional, paramagnetic system to a rapid and arbitrarily large change (quench) in a symmetry-breaking field is investigated. The complete time dependence of the conjugate order parameter is calculated with a real-space renormalization-group (RG) method. The nonlinear relaxation "rate" is found to be time dependent. Its approach to the corresponding prediction of linear-response theory is characterized. The nonlinear response is found to go over to linear response via an early, exponential regime followed by a crossover to an asymptotic, algebraic approach to linear response at long times. The initial transient decay is quench-strength dependent in contrast with the final behavior, which is largely "universal" and quench insensitive. We study a nearest-neighbor Ising model in a magnetic field in the paramagnetic, "disordered" phase. The dynamics are controlled by a kinetic Ising model with simultaneous spin-flip (adsorption-desorption) and spin-exchange (diffusion) kinetics. The model is applicable to non-equilibrium "dosing" experiments on adsorbed systems. Diffusion is shown not to affect the growth rate of the total order parameter (magnetization or coverage). General recursion relations for the temperature and magnetic field are derived for the entire thermodynamic plane. The RG analysis reproduces linear-response theory for arbitrary magnetic field and is consistent with known scaling laws concerning nonlinear relaxation. The time-dependent magnetization in the critical region has a power-law regime before crossing over into its final exponential decay.