Spinodal decomposition and the tomita sum rule

Area of Science:

• Physics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Phase-ordering phenomena are crucial in understanding systems with spontaneous symmetry breaking.
• Conserved order parameters play a key role in the dynamics of these systems.
• Understanding scaling properties is essential for characterizing the late-stage evolution of quenched systems.

Purpose of the Study:

• To investigate the scaling properties of a phase-ordering system with a conserved order parameter.
• To develop a theoretical framework for describing the system's behavior.
• To compare theoretical predictions with numerical results.

Main Methods:

• Development of a theoretical model for phase-ordering dynamics.
• Derivation of scaling functions and analysis of their properties.
• Comparison with existing numerical simulations in three dimensions.

Main Results:

• The developed theory yields scaling functions that satisfy general properties, including the Tomita sum rule.
• Excellent agreement is observed between the theoretical order parameter scaling function and numerical results in three dimensions.
• The nonequilibrium decay exponents are found to be consistent with known lower bounds.

Conclusions:

• The theoretical framework provides a robust description of scaling in conserved phase-ordering systems.
• The findings validate the applicability of the developed theory to real-world physical systems.
• The study contributes to a deeper understanding of critical dynamics and universality classes.