Critical behavior of the two-dimensional Coulomb glass at zero temperature

Abstract

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.

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

“…Recently, we have shown [19] a first-order transition from COP to disordered phase at critical disorder (W c = 0.2253) for two-dimensional CG lattice model at zero temperature. The disorder is in the units of nearest neighbour electron-electron interaction which is taken to be unity (see Sec.3 for details).…”

Effect of increasing disorder on domains of the 2d Coulomb glass

“…At zero disorder and zero temperature, the system is in charge- This discontinuity in staggered magnetization is an indication of first order transition which was confirmed using finite size scaling approach in our previous paper [28]. In that paper, we have used {φ i }'s chosen randomly from a box distribution [−W/2, W/2].…”

“…This corresponds to a transition from charge-ordered phase to disordered phase at W ≈ 0.265. From our previous work [28] we know that as L increases, W c decreases towards W = 0.2253 and the transition becomes sharper. Therefore one expects for larger system sizes, ∆ h ≈ 0 will occur at lower disorder obtained 240 different pseudo ground states.…”

“…The {φ i }'s were chosen in the following manner: for each run, the configuration of signs of the random energies is kept fixed ({φ i } was chosen from a box distribution {−1, 1}) and then multiplied by W/2 where W is the disorder strength, which was increased from 0 to 2. [28], we have chosen more points in the transition region. This approach has an advantage that one is able to see the evolution of domains as W is increased.…”

“…For 2d, at higher disorders Esser et al [27] obtained value of τ = 0.98 and they also classified their domains as fractal. In our previous work [28], we studied a 2d CG lattice model where we have shown a first order transition from charge-ordered phase to disordered phase at zero temperature using finite size scaling. According to our finite size analysis the critical disorder for 64 × 64 system was 0.265.…”