  We report on detailed ac calorimetry measurements under high pressure and
magnetic field of CeRhIn5. Under hydrostatic pressure the antiferromagnetic
order vanishes near p_c*=2 GPa due to a first order transition.
Superconductivity is found for pressures above 1.5 GPa inside the magnetic
ordered phase. However, the superconductivity differ from the pure homogeneous
superconducting ground state above 2 GPa. The application of an external
magnetic field H || ab induces a transition inside the superconducting state
above pc* which is strongly related to the re-entrance of the
antiferromagnetism with field. This field-induced supplementary state vanishes
above the quantum critical point in this system. The analogy to CeCoIn5 is
discussed.
