Aging, phase ordering, and conformal invariance.

Area of Science:

• Statistical physics
• Condensed matter physics
• Dynamical systems

Background:

• Aging phenomena in physical systems often exhibit two-time response function scaling.
• Understanding the universal behavior of these systems is crucial for theoretical advancements.

Purpose of the Study:

• To extend dynamical scaling to conformal invariance.
• To derive the explicit form of the scaling function for aging systems.
• To validate theoretical predictions with numerical and exact results.

Main Methods:

• Theoretical analysis connecting dynamical scaling to conformal invariance.
• Numerical simulations of the 2D and 3D Ising models with Glauber dynamics.
• Exact solutions for the spherical model with nonconserved order parameter.

Main Results:

• The explicit form of the scaling function f(t/s) was derived.
• The theoretical predictions were confirmed in various spin systems.
• Results cover both phase ordering (T

Conclusions:

• Dynamical scaling can be unified with conformal invariance.
• The derived scaling function provides a quantitative description of aging dynamics.
• The findings are robust across different models and interaction ranges.