# Growth Kinetics for a System with Conserved Order Parameter: Off Critical Quenches

Source: [Growth Kinetics for a System with Conserved Order Parameter: Off Critical Quenches](<https://www.sota2.com/research/paper/68fa24122c2a37601939ef72>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T07:55:39.697Z

Authors: G.F. Mazenko, R. A. Wickham

Published: 1994-11-11T03:51:28.000Z

## Abstract

The theory of growth kinetics developed previously is extended to the asymmetric case of off-critical quenches for systems with a conserved scalar order parameter. In this instance the new parameter $M$, the average global value of the order parameter, enters the theory. For $M=0$ one has critical quenches, while for sufficiently large $M$ one approaches the coexistence curve. For all $M$ the theory supports a scaling solution for the order parameter correlation function with the Lifshitz-Slyozov-Wagner growth law $L \\sim t^{1/3}$. The theoretically determined scaling function depends only on the spatial dimensionality $d$ and the parameter $M$, and is determined explicitly here in two and three dimensions. Near the coexistence curve oscillations in the scaling function are suppressed. The structure factor displays Porod's law $Q^{-(d+1)}$ behaviour at large scaled wavenumbers $Q$, and $Q^{4}$ behaviour at small scaled wavenumbers, for all $M$. The peak in the structure factor widens as $M$ increases and develops a significant tail for quenches near the coexistence curve. This is in qualitative agreement with simulations.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9411045>)

[PDF](<https://arxiv.org/pdf/cond-mat/9411045.pdf>)