Renormalization-group theory of spinodal decomposition
Renormalization-group (RG) methods developed previously for the study of the growth of order in unstable systems are extended to treat the spinodal decomposition of the two-dimensional spin-exchange kinetic Ising model. The conservation of the order parameter and fixed-length sum rule are properly preserved in the theory. Various correlation functions in both coordinate and momentum space are calculated as functions of time. The scaling function for the structure factor is extracted. We compare our results with direct Monte Carlo (MC) simulations and find them in good agreement. The time rescaling parameter entering the RG analysis is temperature dependent, as was determined in previous work through a RG analysis of MC simulations. The results exhibit a long-time logarithmic growth law for the typical domain size, both analytically and numerically. In the time region where MC simulations have previously been performed, the logarithmic growth law can be fitted to a power law with an effective exponent. This exponent is found to be in excellent agreement with the result of MC simulations. The logarithmic growth law agrees with a physical model of interfacial motion which involves an interplay between the local curvature and an activated jump across the interface.
- Research Organization:
- The James Franck Institute and The Department of Physics, The University of Chicago, Chicago, Illinois 60637
- OSTI ID:
- 6351092
- Journal Information:
- Phys. Rev. B: Condens. Matter; (United States), Vol. 32:9
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
BINARY ALLOY SYSTEMS
DECOMPOSITION
ISING MODEL
CONSERVATION LAWS
MONTE CARLO METHOD
ORDER PARAMETERS
RENORMALIZATION
SPIN
STRUCTURE FACTORS
SUM RULES
ALLOY SYSTEMS
ANGULAR MOMENTUM
CHEMICAL REACTIONS
CRYSTAL MODELS
EQUATIONS
MATHEMATICAL MODELS
PARTICLE PROPERTIES
360104* - Metals & Alloys- Physical Properties