  In a number of quantum paramagnets, magnetic field can induce a quantum phase
transition to an antiferromagnetic state which exists for a range of fields Hc1
< H < Hc2. Generally, these compounds exhibit a significant asymmetry in their
properties at low- and high-field transitions. Here we present detailed
specific heat and thermal conductivity measurements in NiCl2-4SC(NH2)2 together
with analytical and numerical results. We show that the asymmetry is caused by
a strong renormalization of the effective mass of spin excitations due to
quantum fluctuations for H<Hc1 that are absent for H<Hc2.
