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 [A. Sen and R. Moessner, Phys. Rev. Lett. 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 nonmagnetic impurities. The Metropolis algorithm within a parallel thermal tempering scheme fails to achieve equilibration for this problem already for small system sizes. Motivated by previous work [J. C. Andresen, H. G. Katzgraber, V. Oganesyan and M. Schechter, Phys. Rev. X 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 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, $\nu =1.27\left(8\right)$, and the anomalous exponent, $\eta =0.228\left(35\right)$.

• Received 27 June 2019
• Revised 12 August 2019

DOI:https://doi.org/10.1103/PhysRevB.100.064425