  The superradiant phase transition (SPT) controlled by the interacting
strength between the two-level atom and the photons has been a hot topic in the
Rabi model and the Rabi-dimer model. The latter describes two Rabi cavities
coupled with an inter-cavity hopping parameter. Moreover, the SPT in the
Rabi-dimer model is found to be the same universal class that in the Rabi model
by investigating the correlation-length critical exponent. In this paper, we
are concerned about whether the inter-cavity hopping parameter between two Rabi
cavities (i.e., the Rabi-dimer model) will induce the SPT and to which the
universal class of the phase transition belongs. We analytically derive the
phase boundary of the SPT and investigate the ground-state properties of the
system. We uncover that the inter-cavity induced SPT can be apparently
understood from the ground-state energy and the ground-state photon population,
as well as the ground-state expectation value of the squared anti-symmetric
mode. From the scaling analysis of the fidelity susceptibility, we numerically
verify that the SPT driven by the cavity coupling belongs to the same universal
class as the one driven by the atom-cavity interaction. Our work enriches the
studies on the SPT and its critical behaviors in the Rabi-dimer model.
