Kinetics of the long-range spherical model

TL;DR

This paper investigates the aging dynamics and scaling behavior of the kinetic spherical model with long-range interactions after quenches below and at the critical temperature, comparing results to local scale-invariance predictions.

Contribution

It provides explicit derivations of aging exponents and scaling functions for response and correlation functions in the long-range spherical model.

Findings

Aging exponents are derived for various fields.

Scaling functions match predictions from local scale-invariance.

Results extend understanding of non-equilibrium dynamics in long-range systems.

Abstract

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.