Stress-free Spatial Anisotropy in Phase-Ordering

TL;DR

This paper investigates the emergence of spatial anisotropy in the long-term correlations of two-dimensional Ising models during non-equilibrium phase-ordering, revealing its generic presence across various conditions and its dependence on system specifics.

Contribution

It demonstrates that spatial anisotropy is a common feature in scalar systems with anisotropic surface tension during phase-ordering, regardless of criticality or conservation laws.

Findings

Anisotropy appears in both critical and off-critical quenches.

Anisotropy is present in conserved and non-conserved dynamics.

Correlation functions are non-universal and depend on system parameters.

Abstract

We find spatial anisotropy in the asymptotic correlations of two-dimensional Ising models under non-equilibrium phase-ordering. Anisotropy is seen for critical and off-critical quenches and both conserved and non-conserved dynamics. We argue that spatial anisotropy is generic for scalar systems (including Potts models) with an anisotropic surface tension. Correlation functions will not be universal in these systems since anisotropy will depend on, e.g., temperature, microscopic interactions and dynamics, disorder, and frustration.