Conventional, thermally-driven continuous phase transitions are described by universal critical behaviour that is independent of the specific microscopic details of a material. However, many current studies focus on materials that exhibit quantum-driven continuous phase transitions (quantum critical points, or QCPs) at absolute zero temperature. The classification of such QCPs and the question of whether they show universal behaviour remain open issues. Here we report measurements of heat capacity and de Haas-van Alphen (dHvA) oscillations at low temperatures across a field-induced antiferromagnetic QCP (B$_{c0}simeq$ 50 T) in the heavy-fermion metal CeRhIn$_5$. A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B$_0^*simeq$ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn$_5$ suggest that the Fermi-surface change at B$_0^*$ is associated with a localized to itinerant transition of the Ce-4f electrons in CeRhIn$_5$. Taken in conjunction with pressure data, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn$_5$, a significant step towards the derivation of a universal phase diagram for QCPs.
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