  The lattice model of Coulomb Glass in two dimensions with box-type random
field distribution is studied at zero temperature for system size upto
$96^{2}$. To obtain the minimum energy state we annealed the system using Monte
Carlo simulation followed by further minimization using cluster-flipping. The
values of the critical exponents are determined using the standard finite size
scaling. We found that the correlation length $\xi$ diverges with an exponent
$\nu=1.0$ at the critical disorder $W_{c} = 0.2253$ and that $\chi_{dis}
\approx \xi^{4-\bar{\eta}}$ with $\bar{\eta}=2$ for the disconnected
susceptibility. The staggered magnetization behaves discontinuously around the
transition and the critical exponent of magnetization $\beta=0$. The
probability distribution of the staggered magnetization shows a three peak
structure which is a characteristic feature for the phase coexistence at
first-order phase transition. In addition to this, at the critical disorder we
have also studied the properties of the domain for different system sizes. In
contradiction with the Imry-Ma arguments, we found pinned and non-compact
domains where most of the random field energy was contained in the domain wall.
Our results are also inconsistent with Binder's roughening picture.
