Long-time traces of the initial condition in relaxation phenomena near criticality

Abstract

The time evolution of systems relaxing towards thermal equilibrium is examined near the critical temperature $T_c$, with special attention paid to the role of the initial value $m_i$ of the order parameter $\varphi$. To this end, the $n$-component model A for a cube of length $L$ is investigated. The common belief that all memory of $m_i$ is necessarily lost after a microscopic time span is shown to be unfounded. General arguments and the exact solution of the limit $n\to \infty$ show that $m_i$ leaves its traces in both the linear and nonlinear long-time relaxation of $\varphi$ near or at $T_c$. Specifically for linear relaxation near $T_c$, or at $T_c$ with $L<\infty$, the amplitude of the exponential decay depends on $m_i$ and the short-time exponent ${\theta }^{\prime }=(x_i-x_{\varphi })/z$, provided $t_i\sim m_i^{-z/x_i}$ is comparable to or larger than other time scales. Here $x_i$ is the scaling dimension of $m_i$, $z$ is the dynamic bulk exponent, and $x_{\varphi }$ is the usual equilibrium scaling dimension of $\varphi$.

12 pages, uuencoded postscript file (yesterday an old version of this manuscript was submitted by mistake!!)

Cited by in corpus (21)

• Ageing Properties of Critical Systems
• Dynamic Monte Carlo Measurement of Critical Exponents
• Wilson renormalization of a reaction-diffusion process
• Monte Carlo Simulation of Universal Short-Time Behavior in Critical Relaxation
• Universality and Scaling in Short-time Critical Dynamics
• Finite Size Scaling and Critical Exponents in Critical Relaxation
• Aging in ferromagnetic systems at criticality near four dimensions
• Critical dynamics in thin films
• Near-Surface Long-Range Order at the Ordinary Transition
• Universal Short-Time Behavior in Critical Dynamics near Surfaces
• Critical aging of Ising ferromagnets relaxing from an ordered state
• Universal post-quench coarsening and quantum aging at a quantum critical point
• Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach
• Critical Adsorption in Systems with Weak Surface Field: The Renormalization-Group Approach
• Dynamics of non-Gaussian fluctuations in model A
• Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase
• Near-Surface Long-Range Order at the Ordinary Transition: Scaling Analysis and Monte Carlo Results
• Microscopic Non-Universality versus Macroscopic Universality in Algorithms for Critical Dynamics
• Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
• The role of initial conditions in the ageing of the long-range spherical model
• Fluctuation-dissipation relations in critical coarsening: crossover from unmagnetized to magnetized initial states