  We consider a model of long-range first-passage percolation on the $d$
dimensional square lattice $Z^d$ in which any two distinct vertices $x, y \in
Z^d$ are connected by an edge having exponentially distributed passage time
with mean $||x-y||^{\alpha+o(1)}$, where $\alpha>0$ is a fixed parameter and
$||\cdot||$ is the $\ell_1$-norm on $Z^d$. We analyze the asymptotic growth
rate of the set $B_t$, which consists of all $x \in Z^d$ such that the
first-passage time between the origin 0 and $x$ is at most $t$, as
$t\to\infty$. We show that depending on the values of $\alpha$ there are four
growth regimes:
  (i) instantaneous growth for $\alpha<d$,
  (ii) stretched exponential growth for $\alpha\in (d,2d)$,
  (iii) superlinear growth for $\alpha\in (2d,2d+1)$ and finally
  (iv) linear growth for $\alpha>2d+1$ like the nearest-neighbor first-passage
percolation model corresponding to $\alpha=\infty$.
