In real paramagnets, there is always a subtle many-body contribution to the system's energy, which can be regarded as a small effective local magnetic field (Bloc). Usually, it is neglected, since it is very small when compared with thermal fluctuations and/or external magnetic fields (B). Nevertheless, as both the temperature (T) → 0 K and B → 0 T, such many-body contributions become ubiquitous. Here, employing the magnetic Grüneisen parameter (Γmag) and entropy arguments, we report on the pivotal role played by the mutual interactions in the regime of ultra-low-T and vanishing B. Our key results are: i) absence of a genuine zero-field quantum phase transition due to the presence of Bloc; ii) connection between the canonical definition of temperature and Γmag; and iii) possibility of performing adiabatic magnetization by only manipulating the mutual interactions. Our findings unveil unprecedented aspects emerging from the mutual interactions.