Phase Ordering of 2D XY Systems Below T_{KT}

TL;DR

This paper studies the dynamics of 2D XY systems below the Kosterlitz-Thouless transition after temperature quenches, revealing exact scaling laws and the dependence of autocorrelation decay on initial and final states.

Contribution

It provides an exact treatment of defect-free quenches in 2D XY systems below T_{KT}, deriving scaling laws and autocorrelation decay exponents.

Findings

Correlation length scales as $L(t) \,\propto\, t^{1/2}$ at late times.

Autocorrelation decay exponent depends on initial and final equilibrium exponents.

Exact results for defect-free quenches below T_{KT}.

Abstract

We consider quenches in non-conserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations scale with a characteristic length $L(t) \propto t^{1/2}$ at late times. The autocorrelation decay exponent, $\bar{\lambda} = (\eta_i+\eta_f)/2$, depends on both the initial and the final state of the quench through the respective decay exponents of equilibrium correlations, $C_{EQ}(r) \sim r^{-\eta}$. We also discuss time-dependent quenches.