Metastable and scaling regimes of a one-dimensional Kawasaki dynamics

TL;DR

This paper studies the large-time behavior of a one-dimensional Ising spin chain with complex couplings under Kawasaki dynamics, revealing different scaling regimes and dynamic exponents influenced by metastability and temperature effects.

Contribution

It introduces a detailed analysis of metastable structures and their impact on scaling regimes in Kawasaki dynamics with first- and second-neighbor couplings.

Findings

Different dynamic exponents depend on the ratio and sign of couplings.

At low temperatures, relaxation times are computed using exact diagonalizations.

Without metastability, the dynamics remains diffusive.

Abstract

We investigate the large-time scaling regimes arising from a variety of metastable structures in a chain of Ising spins with both first- and second-neighbor couplings while subject to a Kawasaki dynamics. Depending on the ratio and sign of these former, different dynamic exponents are suggested by finite-size scaling analyses of relaxation times. At low but nonzero-temperatures these are calculated via exact diagonalizations of the evolution operator in finite chains under several activation barriers. In the absence of metastability the dynamics is always diffusive.