We have developed a new technique for measuring the specific heat in very high magnetic fields (35tesla) down to He3 temperature (0.3K). This technique enables high-resolution measurements, typically DC/C~10-4, combined with excellent accuracy ,DC/C~a few%. These instrumental implementations is a powerful tool to study field dependent exotic phenomena; 

I will illustrate these potentialities with new results in the quantum limit of graphite and with the observation of Lifshitz transitions in UCoGe. Finally, a special emphasis will be given on the magnetic phase diagram and quantum criticality of cuprates.