Corrections to scaling in the phase-ordering dynamics of a vector order parameter

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Phase Transitions

Background:

• Phase-ordering kinetics describes how systems with multiple stable phases evolve over time.
• Scaling theories simplify complex systems by relating different states through a characteristic length scale.
• Deviations from ideal scaling behavior can arise from initial conditions and require further analysis.

Purpose of the Study:

• To investigate corrections to scaling in systems with O(n) symmetry at zero temperature.
• To analyze the impact of order parameter deviations on scaling morphology.
• To calculate the correction-to-scaling exponent and function for various system types.

Main Methods:

• Utilizing the approximate Gaussian closure theory developed by Mazenko.
• Calculating the equal-time pair correlation function including scaling corrections.
• Applying methods to both nonconserved and conserved order parameter systems.

Main Results:

• The equal-time pair correlation function was expressed including scaling corrections: C(r,t)=f0(r/L)+L(-omega)f1(r/L).
• The correction-to-scaling exponent (omega) was found to be nontrivial and dependent on system dimensionality (d) and order parameter components (n).
• Exact solutions for corrections to scaling were derived for the nonconserved one-dimensional XY model.

Conclusions:

• Corrections to scaling are significant in phase-ordering kinetics, particularly for systems with O(n) symmetry.
• The derived exponent (omega) and function (f1) provide a more accurate description of system evolution beyond simple scaling.
• The study offers valuable insights into the dynamics of pattern formation and coarsening in complex materials.