  We study numerically the thermodynamic properties of the spin nematic phases
in a magnetic field in the spin-1 bilinear-biquadratic model. When the field is
applied, the phase transition temperature once goes up and then decreases
rapidly toward zero, which is detected by the peak-shift in the specific heat.
The underlying mechanism of the reentrant behavior is the entropic effect. In a
weak field the high temperature paramagnetic phase rapidly loses its entropy
while the ferroquadrupolar nematic phase remains robust by modifying the shape
of the ferroquadrupolar moment. This feature serves as a fingerprint of generic
ferroquadrupolar phases, while it is not observed for the case of
antiferroquadrupoles.
