Critical dynamics in thin films

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.

64 pages, 21 figures

References in corpus (19)

• Critical Phenomena and Renormalization-Group Theory
• Casimir forces in binary liquid mixtures
• Critical phenomena at perfect and non-perfect surfaces
• Monte Carlo Simulation of Universal Short-Time Behavior in Critical Relaxation
• The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
• Critical Dynamics of Magnets
• Kinetics of Phase Separation in Thin Films: Simulations for the Diffusive Case
• Fluctuations of Fluctuation-Induced "Casimir" Forces
• Spin dynamics simulation of the three-dimensional XY model: Structure factor and transport properties
• Universal Short-Time Behavior in Critical Dynamics near Surfaces
• Long-time traces of the initial condition in relaxation phenomena near criticality
• Effective interactions between inclusions in complex fluids driven out of equilibrium
• Finite-Size Effects on Critical Diffusion and Relaxation Towards Metastable Equilibrium
• Scaling of thermal conductivity of helium confined in pores
• Structure factor of thin films near continuous phase transitions
• Dynamic structure factor of the Ising model with purely relaxational dynamics
• Singularity in the boundary resistance between superfluid ${}^4$He and a solid surface
• Finite-size effects on the thermal conductivity of ^4He near T_λ
• Critical Ultrasonics Near the Superfluid Transition : Finite Size Effects

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• Quantum quenches as classical critical films
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• Critical Casimir Effect: Exact Results
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• Relaxation phenomena at criticality
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory
• Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges
• Transient Casimir forces from quenches in thermal and active matter
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Critical adsorption and critical Casimir forces in the canonical ensemble
• Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions
• Generalized Casimir forces in non-equilibrium systems
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
• Non-equilibrium forces following quenches in active and thermal matter
• Casimir force in the O(n -> infinity) model with free boundary conditions
• Forces exerted by a correlated fluid on embedded inclusions
• Exact results for the temperature-field behavior of the Ginzburg-Landau Ising type mean-field model
• Out of equilibrium thermal Casimir effect in a model polarizable material
• Tracer particle in a confined correlated medium: an adiabatic elimination method
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
• Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption
• Simulation of static critical phenomena in non-ideal fluids with the Lattice Boltzmann method
• Inducing oscillations of trapped particles in a near-critical Gaussian field
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
• Casimir Force in a Model with Strongly Adsorbing Competing Walls: Analytical Results
• Fluctuation induced forces in critical films with disorder at their surfaces
• Viscosity of a sheared correlated (near-critical) model fluid in confinement
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• Fluctuations of the critical Casimir force
• Repulsive thermal van der Waals interaction in multi-species asymmetric electrolytes driven by external electric fields
• Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem
• Critical $1$- and $2$-point spin correlations for the $O(2)$ model in $3d$ bounded domains
• Solving Lyapunov equations for electrically driven ternary electrolytes -- application to long-range van der Waals interactions