Supersymmetry at finite temperature

Constructing the temperature-dependent supercharge and Hamiltonian from their expression at zero temperature it has been demonstrated that the supersymmetric graded algebra remains invariant with respect to temperature. Visualizing the effect of temperature on these supersymmetric operators as perturbation, it has been shown that the supersymmetry is broken when these operators or the states (not both) depend on temperature, while it is restored when the mixed picture is taken where the state and operators are both temperature dependent