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Thermodynamic Phase Transition and global stability of the Regular Hayward Black hole Surrounded by Quintessence

In this work, we investigate the thermodynamic and the stability of the regular Hayward black hole surrounded by quintessence. Using the metric of the black hole surrounded by quintessence and the new approach of the holographic principle, we derive the expression of the Unruh Verlinde temperature. Hawking temperature and specific heat are derived using the first law of black holes thermodynamics. Gibbs free energy is also evaluated. The behaviors of these quantities show that, the quantum effects represented by the parameter $β$ induces a decreasing of the Hawking temperature of the black hole, and that decrease is accentuated when increasing the magnitude of $β$ and the normalization factor $a$ related to the density of quintessence. For the lower entropies, the black hole passes from the unstable phase to the stable one by a first order thermodynamics phase transition. When increasing the entropy, a second phase transition occurs. This new phase transition is a second-order thermodynamics phase transition and brings the black hole to unstable state. It results that, when increasing of magnitude of $β$, the phase transition points are shifted to the higher entropies. Moreover, the phenomena of phase transitions are preserved by adding the quintessence. Furthermore, when increasing the normalization factor of quintessence, the first order transition point is shifted to higher entropies, while the second-order thermodynamics phase transition point is shifted to lower entropies.