Universal Short-Time Behavior in Critical Dynamics near Surfaces

TL;DR

This paper investigates the universal short-time critical dynamics near surfaces in classical spin systems, revealing distinct surface exponents and universal power laws through theoretical and computational methods.

Contribution

It introduces a scaling framework for surface critical exponents during short-time dynamics, supported by epsilon-expansion and Monte Carlo simulations.

Findings

Surface critical exponents differ from bulk values.

Universal power-law behavior observed near surfaces.

Scaling relations connect surface and bulk exponents.

Abstract

We study the time evolution of classical spin systems with purely relaxational dynamics, quenched from T >> T_c to the critical point, in the semi-infinite geometry. Shortly after the quench, like in the bulk, a nonequilibrium regime governed by universal power laws is also found near the surface. We show for `ordinary' and `special' transitions that the corresponding critical exponents differ from their bulk values, but can be expressed via scaling relations in terms of known bulk and surface exponents. To corroborate our scaling analysis, we present perturbative (epsilon-expansion) and Monte Carlo results.