  In this letter, using the rainbow functions that were proposed by Magueijo
and Smolin, we investigate the thermodynamics and the phase transition of
rainbow Schwarzschild black hole. First, we calculate the rainbow gravity
corrected Hawking temperature. From this modification, we then derive the local
temperature, free energy, and other thermodynamic quantities in an isothermal
cavity. Finally, we analyze the critical behavior, thermodynamic stability, and
phase transition of the rainbow Schwarzschild black hole. The results show that
the rainbow gravity can stop the Hawking radiation in the final stages of black
holes' evolution and lead to the remnants of black holes. Furthermore, one can
observe that the rainbow Schwarzschild black hole has one first-order phase
transition, two second-order phase transitions, and three Hawking-Page-type
phase transitions in the framework of rainbow gravity theory.
