We investigate the impact of the generalized uncertainty principle to all orders in the Planck length on thermodynamics parameters and on the stability of the Schwarzschild black hole within isothermal cavities. Using the Euclidean action formalism, the thermodynamics properties of the black hole are derived with important corrections compared to the standard case. In particular, we find that the black hole remnant is unstable and may decay to a stable large black hole via a phase transition of first order.
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