Renormalization Group Methods for Prase Separation Problems

Abstract

The kinetic Ising model with both a non-conserved and a conserved order parameter has been extensively studied as a simple representation of the growth kinetics of binary alloys.¹ When the order parameter is not conserved (NCOP), as in an order-disorder transition in a binary alloy, it is well known that the growth kinetics are governed by the curvature-driven dynamics developed by Lifshitz,² Cahn, and Allen³ (LCA), which lead to a growth law for the typical domain size L(t)~t^1/2, as a function of time, for dimensionality greater than one. For a conserved order parameter, (COP) (phase separation or spinodal decomposition in a binary alloy) it has been commonly asserted that the long-time growth kinetics are controlled by the evaporation-condensation mechanism of Lifshitz and Slyozov⁴ which gives L(t)~tⁿ with exponent n=1/3 at least when the concentration of one of the two species is small. However, the available results from experiment, theory, or simulation on the growth law for spinodal decomposition in binary alloys give widely differing exponents⁵ (in the range 0,07 to 0,25) when they are fitted to a power law. There is no hard evidence for any single power law. This points out to the possibility of having a more complicated time dependence in this problem, which appears to be a power law only when a relatively restricted time interval is considered.