Numerical observation of a glassy phase in the three-dimensional Coulomb glass

Abstract

The existence of an equilibrium glassy phase for charges in a disordered potential with long-range electrostatic interactions has remained controversial for many years. Here we conduct an extensive numerical study of the disordertemperature phase diagram of the three-dimensional Coulomb glass model using population annealing Monte Carlo to thermalize the system down to extremely low temperatures. Our results strongly suggest that, in addition to a charge order phase, a transition to a glassy phase can be observed, consistent with previous analytical and experimental studies.

Materials physics and spin glasses

“…Analytic studies have demonstrated mean-field similarity to the SK spin glass and predicted a sharp phase transition to a spin-glass like phase above a critical disorder [38,37]. A recent computer simulation of this case [39] using modern sophisticated scaling tests has demonstrated a sharp transition from plasma/paramagnet to a Coulomb Glass state as temperature is reduced, beyond a sufficient strength of quenched randomness .…”

Charge ordering in the three-dimensional Coulomb glass at finite temperatures and low disorders

“…So like RFIM system there exist two fixed points (W = 0, T = T c ) and (W = W c , T = 0). Both the work on CG model [5,6] shows that the critical exponents for W < W c are similar to the ones at zero temperature fixed point as seen also in RFIM [7][8][9][10]. So it was concluded that at least at small disorders, both CG and RFIM belong to the same universality class One should note that in both these works, the on-site energies are modeled by a Gaussian distribution.…”

“…The phase diagram of the three-dimensional CG model [5,6,11] is quite well established now, suggesting a Charge Ordered (CO) phase below a particular value of disorder (W c ). Since the ground state is antiferromagnetic at zero and small disorders, therefore, the staggered magnetization, M s (which is the difference between two sublattice magnetizations) is the appropriate order parameter here.…”

“…Simulations on three dimensional (3d) CG, modeled using a Gaussian distribution [5,6] have shown a phase diagram similar to the random field Ising model (RFIM). At zero temperature, there exists a critical disorder (W c ) below which one has a charge-ordered (CO) phase, and above it, one finds a disordered phase.…”

“…In this paper we have performed Monte Carlo simulation using Metropolis algorithm on the 3d lattice model at low disorders. Recent studies have used population annealing [6] and exchange method [5] to study the same model. Both these methods are well suited to probe for equilibrium glass transition (W > W c ).…”