Relaxation phenomena at criticality

TL;DR

This paper reviews the universal aspects of non-equilibrium critical dynamics, including aging, scaling, and Casimir forces, with a focus on theoretical models like the Ising model and Gaussian approximations.

Contribution

It provides a comprehensive review of recent theoretical results on universal quantities and phenomena in non-equilibrium critical systems, emphasizing field-theoretical approaches.

Findings

Universal scaling functions and exponents characterize non-equilibrium relaxation.

Casimir-like forces emerge in confined critical systems and evolve over time.

The fluctuation-dissipation ratio is a key universal quantity in these dynamics.

Abstract

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the thermodynamic control parameters. The non-equilibrium evolution following this change displays some of the features typically observed in glassy materials, such as ageing, and it can be monitored via dynamic susceptibilities and correlation functions of the order parameter, the scaling behaviour of which is characterized by universal exponents, scaling functions, and amplitude ratios. This universality allows one to calculate these quantities in suitable simplified models and field-theoretical methods are a natural and viable approach for this analysis. In addition, if a statistical system is spatially confined, universal Casimir-like forces acting on the confining surfaces emerge and they build up in time when the temperature of the system is tuned to its critical value. We review here some of the theoretical results that have been obtained in recent years for universal quantities, such as the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the Ising model with Glauber dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting in a film is discussed within the Gaussian model.