  The Planck length and Planck energy should be taken as invariant scales are
in agreement with various theories of quantum gravity. In this scenario, the
original general relativity can be changed to the so-called gravity's rainbow
which produces significant modifications to the black holes' evolution. In this
paper, using two kinds of rainbow functions, we investigate the thermodynamics
and the phase transition of Schwarzschild black hole in the context of
gravity's rainbow theory. Firstly, with the help of the Heisenberg uncertainty
principle, we calculate the modified Hawking temperature. Then, based on this
modification, we derive the local temperature, free energy and other
thermodynamic quantities in an isothermal cavity. Finally, the critical
behavior, the thermodynamic stability and phase transition of the rainbow
Schwarzschild black hole are analyzed. It turns out that our results are
different from the those of Hawking-Page phase transition. Meanwhile, it is
found that there are many similarities and differences between rainbow
functions I case and rainbow functions II.
