# Effect of increasing disorder on domains of the two-dimensional Coulomb glass

## TL;DR

This study investigates how increasing disorder affects domain structures, phase transitions, and density of states in a two-dimensional Coulomb glass model at near-zero temperature, revealing a first-order transition and deviations from theoretical predictions.

## Contribution

It provides new insights into domain behavior, phase transition nature, and density of states in 2D Coulomb glasses under varying disorder levels, challenging existing theories.

## Key findings

- Energy of domains scales as L^{d-1}
- First-order transition indicated by magnetization discontinuity
- Density of states transitions from hard to soft gap with disorder

## Abstract

We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at $T\sim 0$. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using Baranovskii et al algorithm followed by cluster flipping to obtain the pseudo ground states. 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 random field Ising model, one gets critical dimension $d_{c}\geq 2$ for Coulomb glass. The investigations of domains in the transition region shows a discontinuity in staggered magnetization which is an indication of a first-order type transition from charge-ordered phase to disordered phase. The structure and nature of Random field fluctuations of the second largest domain in Coulomb glass are inconsistent with the assumptions of Imry and Ma as was also reported for random field Ising model. The study of domains showed that in the transition region there were mostly two large domains and as disorder was increased, the two large domains remained but there were a large number of small domains. We have also studied the properties of the second largest domain as a function of disorder. We furthermore analysed the effect of disorder on the density of states and showed a transition from hard gap at low disorders to a soft gap at higher disorders. At $W=2$, we have analysed the soft gap in detail and found that the density of states deviates slightly ($\delta\approx 1.293 \pm 0.027$) from the linear behaviour in two dimensions. Analysis of local minima show that the pseudo ground states have similar structure.