The real interaction between matter and electromagnetic radiation is too complicated for a complete theoretical investigation. In this paper, we study phase transition of polariton and magnetopolariton in semiconductor microcavity. We have analyzed the polariton and magnetopolariton phase transition via the path integral approach in Dicke model. Numerical results showed that the system exhibits phase transition from normal phase to super-radiant phase. The transition is affected by the coupling term, Matsubara frequencies and temperature. We observed that the sudden transition is closed to absolute temperature, which means that these three parameters have considerable effect on the polariton formation and stability. Additionally, the introduction of the magnetic field in the semiconductor microcavity shows that the system still undergoes a phase transition. It is shown that weak magnetic field does not alter the phase transition significantly, apart from a small shift of the transition point. Compared to other parameters strong magnetic field drastically change sign at the critical temperature.

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