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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 [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 << 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).