  We investigate the criticality of chiral phase transition manifested in the
first and second order derivatives of Dirac eigenvalue spectrum with respect to
light quark mass in (2+1)-flavor lattice QCD. Simulations are performed at
temperatures from about 137 MeV to 176 MeV on $N_{\tau}=8$ lattices using the
highly improved staggered quarks and the tree-level improved Symanzik gauge
action. The strange quark mass is fixed to its physical value
$m_s^{\text{phy}}$ and the light quark mass is set to $m_s^{\text{phy}}/40$
which corresponds to a Goldstone pion mass $m_{\pi}=110$ MeV. We find that in
contrast to the case at $T\simeq 205$ MeV $m_l^{-1} \partial \rho(\lambda,
m_l)/\partial m_l$ is no longer equal to $\partial ^2\rho(\lambda,
m_l)/\partial m_l^2$ and $\partial ^2\rho(\lambda, m_l)/\partial m_l^2$ even
becomes negative at certain low temperatures. This means that as temperature
getting closer to $T_c$ $\rho(\lambda, m_l)$ is no longer proportional to
$m_l^2$ and thus dilute instanton gas approximation is not valid for these
temperatures. We demonstrate the temperature dependence can be factored out in
$\partial \rho(\lambda, m_l)/ \partial m_l$ and $\partial^2 \rho(\lambda, m_l)/
\partial m_l^2$ at $T \in [137, 153]$ MeV, and then we propose a feasible
method to estimate the power $c$ given $\rho \propto m_l^{c}$.
