  We prove an optimal $O(n \log n)$ mixing time of the Glauber dynamics for the
Ising models with edge activity $\beta \in \left(\frac{\Delta-2}{\Delta},
\frac{\Delta}{\Delta-2}\right)$. This mixing time bound holds even if the
maximum degree $\Delta$ is unbounded.
  We refine the boosting technique developed in [CFYZ21], and prove a new
boosting theorem by utilizing the entropic independence defined in [AJK+21].
The theorem relates the modified log-Sobolev (MLS) constant of the Glauber
dynamics for a near-critical Ising model to that for an Ising model in a
sub-critical regime.
