Convergence of the enhancement of the effective mass under pressure and magnetic field in heavy-fermion compounds: CeRu2Si2, CeRh2Si2, and CeIn3

Emphasis is given on the observation of a convergence to a critical value of the effective mass of a heavy fermion compound by tuning it through a quantum instability either by applying pressure or magnetic field from an antiferromagnetic (AF) to a paramagnetic (PM) ground state. Macroscopic and microscopic results are discussed and the main message is to rush to the discovery of an ideal material whose Fermi surface could be fully observed on both sides of each quantum phase transition.