Local aging phenomena close to magnetic surfaces

TL;DR

This paper investigates surface aging phenomena in semi-infinite Ising models, revealing distinct surface exponents and aging behaviors compared to bulk, through exact solutions and extensive numerical simulations.

Contribution

It provides the first exact solution for the semi-infinite Ising model in large dimensions and extensive numerical analysis of surface aging in two dimensions.

Findings

Surface exponents differ from bulk values.

Surface autocorrelation exponent $b_1$ vanishes in 2D.

Finite-time corrections significantly affect observed scaling.

Abstract

Surface aging phenomena are discussed for semi-infinite systems prepared in a fully disordered initial state and then quenched to or below the critical point. Besides solving exactly the semi-infinite Ising model in the limit of large dimensions, we also present results of an extensive numerical study of the nonequilibrium dynamical behavior of the two-dimensional semi-infinite Ising model undergoing coarsening. The studied models reveal a simple aging behavior where some of the nonequilibrium surface exponents take on values that differ from their bulk counterparts. For the two-dimensional semi-infinite Ising model we find that the exponent $b_1$, that describes the scaling behavior of the surface autocorrelation, vanishes. These simulations also reveal the existence of strong finite-time corrections that to some extent mask the leading scaling behavior of the studied two-time quantities.