Thermal properties of parasupersymmetric oscillator

Parasupersymmetric oscillator model of one bosonic and one order p parafermionic degrees of freedom at finite temperature is investigated in the framework of Thermo Field Dynamics (TFD). In this paper, the temperature dependent vacuum |O(β)right-angle is constructed and the generator of thermal unitary transformation |O(β)right-angle = e- iG(β)|O right-angle is obtained. The authors also comment on a signal of the parasupersymmetry breaking at finite temperature