  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.
