  We investigate the influence of light-matter interactions on correlated
quantum matter by studying the paradigmatic Ising model subject to a quantum
Rabi coupling. This type of coupling to a confined, spatially delocalized
bosonic light mode, such as provided by an optical resonator, resembles a
quantized transverse magnetic field of tunable strength. As a consequence, the
symmetry-broken magnetic state breaks down for strong enough light-mater
interactions to a paramagnetic state. The non-local character of the bosonic
mode can change the quantum phase transition in a drastic manner, which we
analyze quantitatively for the simplest case of a chain geometry (Dicke-Ising
chain). The results show a direct transition between a magnetically ordered
phase with zero photon density and a magnetically polarized phase with lasing
behaviour of the light. Our predictions are equally valid for the dual
quantized Ising chain in a conventional transverse magnetic field.
