Universality in the Dynamics of Second-Order Phase Transitions

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Non-equilibrium Dynamics

Background:

• Topological defects are crucial in understanding symmetry-breaking phase transitions.
• Their formation dynamics, particularly the dependence on quench rates, are often described by power laws.
• Existing methods rely on physical arguments, lacking a unified analytical framework.

Purpose of the Study:

• To propose a general analytical approach for deriving scaling laws of topological defect formation.
• To provide a method independent of specific physical assumptions or approximations.
• To demonstrate the approach's applicability in both homogeneous and nonhomogeneous systems.

Main Methods:

• Analytical transformation of equations of motion to a universal form.
• Derivation of scaling laws based on this universal form.
• Application to systems undergoing symmetry-breaking second-order phase transitions.

Main Results:

• A general method for deriving defect number scaling laws is presented.
• The approach successfully predicts power-law dependencies on quench rates.
• The method is validated for both homogeneous and nonhomogeneous scenarios.

Conclusions:

• The proposed analytical approach offers a rigorous framework for understanding defect formation dynamics.
• This method provides a universal perspective on topological defect scaling across different physical systems.
• The approach's generality allows for potential extensions to other non-equilibrium phenomena.