We have measured the magnetic field dependence of the paramagnetic to the field-induced high temperature antiferroquadrupolar magnetically ordered phase transition is CeB6 from 0 to 60 T using a variety of techniques. It is found that the field-dependent phase separation line becomes re-entrant above 35 T and below 10 K. Measurements of resonant ultra-sound, specific heat and neutron diffraction show conclusively that the zero-field temperature-dependent phase transition is to a state with no ordered dipole moments, but with second order transition signatures in both sound attenuation and specific heat.
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