Using novel instrumentation to combine extreme conditions of intense pulsed magnetic field up to 60~T and high pressure up to 4~GPa, we have established the three-dimensional (3D) magnetic field - pressure - temperature phase diagram of a pure stoichiometric heavy-fermion antiferromagnet (CeRh$_2$Si$_2$). We find a temperature- and pressure-dependent decoupling of the critical and pseudo-metamagnetic fields, at the borderlines of antiferromagnetism and strongly-correlated paramagnetism. This 3D phase diagram is representative of a class of heavy-fermion Ising antiferromagnets, where long-range magnetic ordering is decoupled from a maximum in the magnetic susceptibility. The combination of extreme conditions enabled us to characterize different quantum phase transitions, where peculiar quantum critical properties are revealed. The interest to couple the effects of magnetic field and pressure on quantum-critical correlated-electron systems is stressed.
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