Out-of-equilibrium properties of the semi-infinite kinetic spherical model

TL;DR

This paper investigates the out-of-equilibrium dynamics of the semi-infinite kinetic spherical model at criticality and low temperature, focusing on surface properties and boundary conditions, with explicit calculations of fluctuation-dissipation ratios and scaling functions.

Contribution

It provides explicit analytical results for surface fluctuation-dissipation ratios and scaling functions in the kinetic spherical model under different boundary conditions.

Findings

Surface fluctuation-dissipation ratio determined explicitly

Scaling functions of two-time surface correlations and responses derived

Surface exponent $b_1$ differs from bulk value under Dirichlet conditions in low-temperature phase

Abstract

We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase, both for Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation ratio and the scaling functions of two-time surface correlation and response functions are determined explicitly in the dynamical scaling regime. In the low-temperature phase our results show that for the case of Dirichlet boundary conditions the value of the non-equilibrium surface exponent $b_1$ differs from the usual bulk value of systems undergoing phase ordering.