Dynamical scaling: the two-dimensional XY model following a quench

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics

Background:

• The two-dimensional XY model is a fundamental system for studying phase transitions and critical phenomena.
• Quenching from high temperatures into an ordered phase induces complex dynamics and scaling behavior.

Purpose of the Study:

• To rigorously test dynamical scaling in the 2D XY model after a temperature quench.
• To compare measured correlations with theoretical approximations and analyze length-scale dependencies.

Main Methods:

• Investigating the difference between measured correlations and Gaussian-closure approximation results.
• Direct comparison of various length scales to identify scaling behavior.
• Reconstructing correlations from minimal-energy configurations based on vortex positions.

Main Results:

• Observed results are consistent with dynamical scaling and an asymptotic growth law L ~ (t/ln[t/t(0)])^(1/2).
• The time scale t(0) was found to be length-dependent.
• Reconstructed correlations differed significantly from "natural" correlations, yet both scaled with L.

Conclusions:

• Both topological (vortex) and nontopological (spin-wave) contributions are relevant to correlations long after quenching.
• A generalized definition of dynamical scaling was presented, applicable to other quenched systems.
• The approach is directly applicable to planar liquid-crystal systems.