in magnetic field*

We measured specific heat of the pyrochlore Ce₂Zr₂O₇ in magnetic field up to 14 T and temperatures down to 60 mK. In zero field we observe a monotonic rise of the specific heat, with the values of C/T reaching 30 J/mol-K at 100 mK, and without saturation, at least in some compounds. The field was applied in either [100] or [110] directions. Even small magnetic field on the order of a kilogauss pushes the entropy up in temperature, developing a broad maximum in C(T), which moves up in temperature with increasing magnetic field. The calculated entropy is consistent with a doublet ground state. Extreme sensitivity to small magnetic field is consistent with a disordered zero-field ground state, with entropy piling up towards T=0, indicating a possible spin-liquid.