Finite temperature phase transition in the two-dimensional Coulomb glass at low disorders

We present numerical evidence using Monte Carlo simulations of finite-temperature phase transition in two dimensional Coulomb Glass lattice model with random site energies at half-filling. For the disorder strengths ($W$) studied in this paper, we find the existence of charge-ordered phase (COP) below the critical temperature ($T_{c}(W)$). Also, the probability distribution of staggered magnetization calculated at each W shows a two-peak structure at their respective critical temperature. Thus the phase transition from fluid to COP as a function of temperature is second order for all $W$. We find no evidence of a spin glass phase between a fluid and the COP. Further, we have used a finite-size scaling analysis to calculate the critical exponents. The critical exponents at zero disorder are different from the one found at finite disorders, which indicates that the disorder is a relevant parameter here. The critical exponent for correlation length of $\nu$ increases and $T_{c}$ decreases with increasing disorder. Similar behaviour for $\nu$ was seen in the work of Overlin et al for three dimensional Coulomb Glass model with a positional disorder. Our study also shows that other critical exponents are also a function of the disorder.