Revisiting Kawasaki dynamics in one dimension

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 ≃ 3.11 for instant quenches under ferromagnetic couplings, while approaching to z ≃ 2 in the antiferro case. The spin representation complements the evaluation of dynamic exponents at higher temperature scales, where the kinetics still remains slow.