# Corrections to Scaling in Phase-Ordering Kinetics

Source: [Corrections to Scaling in Phase-Ordering Kinetics](<https://www.sota2.com/research/paper/68fa24682c2a3760193a3a6e>)

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

Data updated: 2025-10-24T09:08:56.559Z

Authors: A.J. Bray, P.N. Rapapa, S.J. Cornell

Published: 1997-09-19T16:27:22.000Z

## Abstract

The leading correction to scaling associated with departures of the initial condition from the scaling morphology is determined for some soluble models of phase-ordering kinetics. The result for the pair correlation function has the form C(r,t) = f\_0(r/L) + L^{-\\omega} f\_1(r/L) + ..., where L is a characteristic length scale extracted from the energy. The correction-to-scaling exponent \\omega has the value \\omega=4 for the d=1 Glauber model, the n-vector model with n=\\infty, and the approximate theory of Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \\omega has a non-trivial value: omega = 3.8836... for d=2, and \\omega = 3.9030... for d=3. The correction-to-scaling functions f\_1(x) are also calculated.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9709213>)

[PDF](<https://arxiv.org/pdf/cond-mat/9709213.pdf>)