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

TL;DR

This study uses Monte Carlo simulations to demonstrate a second-order phase transition to a charge-ordered phase in a two-dimensional Coulomb glass model at finite temperature, with critical behavior influenced by disorder strength.

Contribution

First numerical evidence of a finite-temperature second-order phase transition in 2D Coulomb glass with disorder, including critical exponents and disorder dependence.

Findings

Charge-ordered phase exists below critical temperature for studied disorders.

Phase transition is second order, with no spin glass phase observed.

Critical exponents vary with disorder strength, indicating disorder relevance.

Abstract

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 charge-ordered 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 a finite-size 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 of $\nu$ increases and $T_{c}$ decreases with increasing disorder. Similar behaviour for $\nu$ 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 the disorder.