Effect of weak disorder on the ground state of uniaxial dipolar spin systems in the upper critical dimension

TL;DR

This study uses Monte Carlo simulations to examine how weak quenched disorder affects the ferromagnetic ground state of three-dimensional uniaxial dipolar spin systems, revealing its robustness in the upper critical dimension.

Contribution

It provides a finite-size scaling analysis with logarithmic corrections for pure systems and demonstrates the irrelevance of weak disorder in maintaining ferromagnetic order.

Findings

Weak disorder does not destabilize the ferromagnetic ground state.

Finite-size scaling with logarithmic corrections accurately describes the system.

The disorder-temperature phase diagram shows ferromagnetism persists with small disorder.

Abstract

Extensive Monte Carlo simulations are used to investigate the stability of the ferromagnetic ground state in three-dimensional systems of Ising dipoles with added quenched disorder. These systems model the collective ferromagnetic order observed in various systems with dipolar long-range interactions. The uniaxial dipolar spins are arranged on a face-centred cubic lattice with periodic boundary conditions. Finite-size scaling relations for the pure dipolar ferromagnetic system are derived by a renormalisation group calculation. These functions include logarithmic corrections to the expected mean field behaviour since the system is in its upper critical dimension. Scaled data confirm the validity of the finite-size scaling description and results are compared with subsequent analysis of weakly disordered systems. A disorder-temperature phase diagram displays the preservation of the ferromagnetic ground state with the addition of small amounts of disorder, suggesting the irrelevance of weak disorder in these systems.