# The dipolar spin glass transition in three dimensions

## TL;DR

This paper investigates the existence of a finite-temperature spin glass transition in a three-dimensional dilute dipolar Ising system, introducing an improved Monte Carlo algorithm to overcome equilibration challenges and providing critical exponent estimates.

## Contribution

The authors develop a specialized cluster Monte Carlo algorithm for dilute dipolar Ising systems and demonstrate a finite-temperature spin glass transition with estimated critical exponents.

## Key findings

- Finite-temperature spin glass transition confirmed.
- Critical exponents estimated: ν=1.27(8), η=0.228(35).
- Universality appears independent of impurity concentration x for small x.

## Abstract

Dilute dipolar Ising magnets remain a notoriously hard problem to tackle both analytically and numerically because of long-ranged interactions between spins as well as rare region effects. We study a new type of anisotropic dilute dipolar Ising system in three dimensions [Phys. Rev. Lett. {\bf 114}, 247207 (2015)] that arises as an effective description of randomly diluted classical spin ice, a prototypical spin liquid in the disorder-free limit, with a small fraction $x$ of non-magnetic impurities. Metropolis algorithm within a parallel thermal tempering scheme fails to achieve equilibration for this problem already for small system sizes. Motivated by previous work [Phys. Rev. X {\bf 4}, 041016 (2014)] on uniaxial random dipoles, we present an improved cluster Monte Carlo algorithm that is tailor-made for removing the equilibration bottlenecks created by clusters of {\it effectively frozen} spins. By performing large-scale simulations down to $x=1/128$ and using finite size scaling, we show the existence of a finite-temperature spin glass transition and give strong evidence that the universality of the critical point is independent of $x$ when it is small. In this $x \ll 1$ limit, we also provide a first estimate of both the thermal exponent, $\nu=1.27(8)$, and the anomalous exponent, $\eta=0.228(35)$.