Critical dynamics in thin films

TL;DR

This paper analyzes the critical dynamics of thin films using a field-theoretical approach, focusing on relaxational dynamics, boundary effects, and fluctuation-induced forces, providing universal scaling functions and exploring nonlinear relaxation.

Contribution

It offers new analytic expressions for universal scaling functions in critical thin film dynamics under Dirichlet boundary conditions, including effects of time-dependent fields and nonlinear relaxation.

Findings

Derived universal scaling functions for response and correlation in thin films.

Quantified effects of time-dependent fields on dynamic Casimir forces.

Analyzed nonlinear relaxation crossover behaviors.

Abstract

Critical dynamics in film geometry is analyzed within the field-theoretical approach. In particular we consider the case of purely relaxational dynamics (Model A) and Dirichlet boundary conditions, corresponding to the so-called ordinary surface universality class on both confining boundaries. The general scaling properties for the linear response and correlation functions and for dynamic Casimir forces are discussed. Within the Gaussian approximation we determine the analytic expressions for the associated universal scaling functions and study quantitatively in detail their qualitative features as well as their various limiting behaviors close to the bulk critical point. In addition we consider the effects of time-dependent fields on the fluctuation-induced dynamic Casimir force and determine analytically the corresponding universal scaling functions and their asymptotic behaviors for two specific instances of instantaneous perturbations. The universal aspects of nonlinear relaxation from an initially ordered state are also discussed emphasizing the different crossovers that occur during this evolution. The model considered is relevant to the critical dynamics of actual uniaxial ferromagnetic films with symmetry-preserving conditions at the confining surfaces and for Monte Carlo simulations of spin system with Glauber dynamics and free boundary conditions.