Comparative Study of Optimization of Electron Glass using Extremal and Quenching Algorithms

In this work, we have used quenching by Monte Carlo simulation and extremal optimization to find the ground state of the electron glass model in two dimensions at small disorders. In the electron glass model, the electrons interact via unscreened Coulomb interaction, and the number of electrons is conserved. This implies that the interaction is long-ranged. Extremal optimization is an efficient algorithm used to find the ground state of many short-ranged disordered systems like spin glass and random field Ising model. In this paper, we extend this algorithm to find the ground states of the long-range electron glass system. We have also quenched the system to small temperatures using Monte Carlo simulation to obtain the ground state. Since the electron number is conserved, the system evolves using Kawasaki dynamics. We show that the efficiency of extremal optimization is more than the quenching method. For both methods, the efficiency decreases as the disorder is increased. The metastable states formed are very long-lived and consist of large domains which are very stable.