Revisiting Kawasaki dynamics in one dimension

TL;DR

This paper numerically re-examines the critical exponents of Kawasaki dynamics in a one-dimensional Ising model, revealing different dynamical behaviors in ferromagnetic and antiferromagnetic regimes at various temperatures.

Contribution

It provides a detailed numerical analysis of the spectrum gap in both spin and domain wall representations, offering new insights into the dynamics at different temperature regimes.

Findings

In ferromagnetic case, the dynamical exponent z ≈ 3.11 at low temperature.

In antiferromagnetic case, the exponent approaches z ≈ 2.

Domain wall representation converges rapidly at low temperatures.

Abstract

Critical exponents of the Kawasaki dynamics in the Ising chain are re-examined numerically through the spectrum gap of evolution operators constructed both in spin and domain wall representations. At low temperature regimes the latter provides a rapid finite-size convergence to these exponents, which tend to $z \simeq 3.11$ for instant quenches under ferromagnetic couplings, while approaching to $z \simeq 2$ in the antiferro case. The spin representation complements the evaluation of dynamic exponents at higher temperature scales, where the kinetics still remains slow.