Physics – Condensed Matter
Scientific paper
1994-09-14
Phys. Rev. E 51 (1995) 5392
Physics
Condensed Matter
12 pages, uuencoded postscript file (yesterday an old version of this manuscript was submitted by mistake!!)
Scientific paper
10.1103/PhysRevE.51.5392
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 $\phi$. 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 $\phi$ 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 $\theta'=(x_i-x_{\phi})/z$, 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 $x_{\phi}$ is the usual equilibrium scaling dimension of $\phi $.
Diehl H. W.
Ritschel Uwe
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