  We investigate the influence of long-range (LR) interactions on the phase
ordering dynamics of the one-dimensional random field Ising model (RFIM).
Unlike the usual RFIM, a spin interacts with all other spins through a
ferromagnetic coupling that decays as $r^{-(1+\sigma)}$, where $r$ is the
distance between two spins. In the absence of LR interactions, the size of
coarsening domains $R(t)$ exhibits a crossover from pure system behavior $R(t)
\sim t^{1/2}$ to an asymptotic regime characterized by logarithmic growth:
$R(t) \sim (\ln t)^2$. The LR interactions affect the pre-asymptotic regime,
which now exhibits ballistic growth $R(t) \sim t$, followed by
$\sigma$-dependent growth $R(t) \sim t^{1/(1+\sigma)}$. Additionally, the LR
interactions also affect the asymptotic logarithmic growth, which becomes $R(t)
\sim (\ln t)^{\alpha(\sigma)}$ with $\alpha(\sigma) < 2$. Thus, LR interactions
lead to faster growth than for the nearest-neighbor system at short times.
Unexpectedly, this driving force causes a slowing-down of the dynamics ($\alpha
< 2$) in the asymptotic logarithmic regime. This is explained in terms of a
non-trivial competition between the pinning force caused by the random field
and the driving force introduced by LR interactions. We also study the spatial
correlation function and the autocorrelation function of the magnetization
field. The former exhibits superuniversality for all $\sigma$, i.e., a scaling
function that is independent of the disorder strength. The same holds for the
autocorrelation function when $\sigma<1$, whereas a signature of the violation
of superuniversality is seen for $\sigma>1$.
