Recent advances in nanofabrication and optical control have garnered tremendous interest in multi-qubit-cavity systems. Here we analyze a spin-glass version of such a nanostructure, solving analytically for the phase diagrams in both the matter and radiation subsystems in the replica symmetric regime. Interestingly, the resulting phase transitions turn out to be tunable simply by varying the matter-radiation coupling strength. Copyright (C) EPLA, 2008.