Aging phenomena in critical semi-infinite systems

TL;DR

This paper investigates aging phenomena at surfaces of semi-infinite critical systems through numerical analysis of autocorrelation and autoresponse functions, revealing how surface critical exponents influence dynamic scaling and fluctuation-dissipation ratios.

Contribution

It provides a systematic numerical study of surface aging in semi-infinite critical systems, including models with continuously varying surface critical exponents, and compares results with local scale invariance predictions.

Findings

Surface two-time quantities follow scaling laws consistent with local scale invariance.

Surface fluctuation-dissipation ratios depend on surface critical exponents.

Surface aging behavior varies with model parameters and dimensions.

Abstract

Nonequilibrium surface autocorrelation and autoresponse functions are studied numerically in semi-infinite critical systems in the dynamical scaling regime. Dynamical critical behaviour is examined for a nonconserved order parameter in semi-infinite two- and three-dimensional Ising models as well as in the Hilhorst-van Leeuwen model. The latter model permits a systematic study of surface aging phenomena, as the surface critical exponents change continuously as function of a model parameter. The scaling behaviour of surface two-time quantities is investigated and scaling functions are confronted with predictions coming from the theory of local scale invariance. Furthermore, surface fluctuation-dissipation ratios are computed and their asymptotic values are shown to depend on the values of surface critical exponents.