  Matrix models for the deconfining phase transition in $SU(N)$ gauge theories
have been developed in recent years. With a few parameters, these models are
able to reproduce the lattice results of the thermodynamic quantities in the
semi-quark gluon plasma(QGP) region. They are also used to compute the behavior
of the 't Hooft loop and study the exceptional group $G(2)$. In this paper, we
review the basic ideas of the construction of these models and propose a new
form of the non-ideal corrections in the matrix model. In the semi-QGP region,
our new model is in good agreement with the lattice simulations as the previous
ones, while in higher temperature region, it reproduces the upward trend of the
rescaled trace anomaly as found in lattice which, however, can not be obtained
from the previous models. In addition, we discuss the perturbative corrections
to the thermal effective potential which could be used to systematically
improve the matrix models at high temperatures. In particular, we provide, for
the first time, an analytical proof of the relation between the one- and
two-loop effective potential: two-loop correction is proportional to the
one-loop result, independent of the eigenvalues of the Polyakov loop. This is a
very general result, we prove it for all classic groups, including $SU(N)$,
$SO(2N+1)$, $SO(2N)$ and $Sp(2N)$.
