Absence of Dipole Glass Transition for Randomly Dilute Classical Ising Dipoles

TL;DR

This study uses Monte Carlo simulations to show that dilute three-dimensional dipolar systems do not exhibit a spin glass transition at low concentrations, with the transition temperature approaching zero as system size increases.

Contribution

It provides evidence that dilute classical Ising dipoles in three dimensions do not undergo a glass transition, challenging previous expectations.

Findings

Transition temperature T_g approaches zero as 1/√N

Entropy per particle is higher at lower concentrations

No phase transition observed at low concentrations

Abstract

Dilute dipolar systems in three dimensions are expected to undergo a spin glass transition as the temperature decreases. Contrary to this, we find from Wang-Landau Monte Carlo simulations that at low concentrations $x$, dipoles randomly placed on a cubic lattice with dipolar interactions do not undergo a phase transition. We find that in the thermodynamic limit the ``glass'' transition temperature $T_g$ goes to zero as $1/\sqrt{N}$ where $N$ is the number of dipoles. The entropy per particle at low temperatures is larger for lower concentrations ($x=4.5%$) than for higher concentrations ($x=20%$).