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 clusterflipping. The values of the critical exponents are determined using the standard finite size scaling. We found that the correlation length ξ diverges with an exponent ν = 1.0 at the critical disorder Wc = 0.2253 and that χ dis ≈ ξ 4−η withη = 2 for the disconnected susceptibility. The staggered magnetization behaves discontinuously around the transition and the critical exponent of magnetization β = 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 noncompact domains where most of the random field energy was contained in the domain wall. Our results are also inconsistent with Binder's roughening picture.
We have annealed two dimensional lattice model of Coulomb glass using Monte Carlo simulations to obtain the minimum energy state (referred to as ground state). We have shown that the energy required to create a domain of linear size L in d dimensions is proportional to L d−1 . Using Imry-Ma arguments given for RFIM, one gets critical dimension dc ≥ 2 for Coulomb glass. The investigations in the transition region shows that the domain wall of the metastable state in the charge-ordered phase shifts as disorder is increased to give disordered ground state at higher disorder strength indicating phase coexistence. This coupled with discontinuity in magnetization is an indication of first-order type transition from charge-ordered phase to disordered phase. The structure and nature of Random field fluctuations of the domain in Coulomb glass are inconsistent with the assumptions of Imry and Ma as was also reported for RFIM.
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 chargeordered 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 finitesize 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 ν increases and T c decreases with increasing disorder. Similar behaviour for ν 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 disorder.
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