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We study a generic model of globally coupled rotors that includes the effectsof noise, phase shift in the coupling, and distributions of moments of inertiaand natural frequencies of oscillation. As particular cases, the setup includespreviously studied Sakaguchi-Kuramoto, Hamiltonian and Brownian mean-field, andTanaka-Lichtenberg-Oishi and Acebr\'on-Bonilla-Spigler models. We derive anexact solution of the self-consistent equations for the order parameter in thestationary state, valid for arbitrary parameters in the dynamics, anddemonstrate nontrivial phase transitions to synchrony that include reentrantsynchronous regimes.

Synchronization transitions in globally coupled rotors in presence of noise and inertia: Exact results