  Using a variational approach we investigate the delocalized to localized
crossover in the ground state of an Ohmic two-impurity spin-boson model,
describing two otherwise non-interacting spins coupled to a common bosonic
environment. We show that a competition between an environment-induced Ising
spin interaction and externally applied fields leads to variations in the
system-bath coupling strength, $\alpha_c$, at which the delocalized-localized
crossover occurs. Specifically, the crossover regime lies between
$\alpha_c=0.5$ and $\alpha_c=1$ depending upon the spin separation and the
strength of the transverse tunneling field. This is in contrast to the
analogous single spin case, for which the crossover occurs (in the scaling
limit) at fixed $\alpha_c\approx1$. We also discuss links between the
two-impurity spin-boson model and a dissipative two-spin transverse Ising
model, showing that the latter possesses the same qualitative features as the
Ising strength is varied. Finally, we show that signatures of the crossover may
be observed in single impurity observables, as well as in the behaviour of the
system-environment entanglement.
