  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 $\beta$
induces a decreasing of the Hawking temperature of the black hole, and that
decrease is accentuated when increasing the magnitude of $\beta$ 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 $\beta$, 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.
