# Critical behaviour in two-dimensional Coulomb Glass at zero temperature

## TL;DR

This study investigates the zero-temperature phase transition in a two-dimensional Coulomb Glass model, revealing a first-order transition with phase coexistence, critical exponents, and domain properties that challenge existing theoretical predictions.

## Contribution

The paper provides the first detailed numerical analysis of the critical behavior and domain structures in 2D Coulomb Glass at zero temperature, highlighting deviations from traditional theories.

## Key findings

- Correlation length diverges with exponent ν=1.0 at critical disorder
- Discontinuous behavior of staggered magnetization with β=0
- Presence of pinned, non-compact domains contradicting Imry-Ma and Binder's theories

## 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 cluster-flipping. The values of the critical exponents are determined using the standard finite size scaling. We found that the correlation length $\xi$ diverges with an exponent $\nu=1.0$ at the critical disorder $W_{c} = 0.2253$ and that $\chi_{dis} \approx \xi^{4-\bar{\eta}}$ with $\bar{\eta}=2$ for the disconnected susceptibility. The staggered magnetization behaves discontinuously around the transition and the critical exponent of magnetization $\beta=0$. 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 non-compact domains where most of the random field energy was contained in the domain wall. Our results are also inconsistent with Binder's roughening picture.