Harnessing finite-size effects to gauge aging in the 2D Ising model

The relaxation behavior towards equilibrium of the 2D Ising model with nearest-neighbor interactions has been studied with focus on the two-time autocorrelator C ( t , s ) . Finite-size effects affecting the growing magnetic domains lead to the saturation of C ( t , s ) with a distinct plateau of height C ∞ ( 2 ) ( s , L ) scaling algebraically with waiting time s and lattice size L . These scaling relations are used to produce precise estimates for the autocorrelation exponent λ and dynamical exponent z with deliberately small lattices. Treating smooth domain walls in a similar manner to the lattice boundaries, their effect on C ( t , s ) can be understood as premature finite-size phenomenon, extending our ansatz to systems not yet in equilibrium.