Loop-string algorithm for Monte Carlo simulations of dipolar spin ice

Recently, we proposed the loop-string algorithm (LSA) for the Monte Carlo simulations of the nearest-neighbor (NN) spin-ice model [Phys. Rev. B 90, 220406(R) (2014)]. Here we discuss its advancement to a dipolar spin ice (DSI) such as Ho2Ti2O7 and Dy2Ti2O7. For this purpose, based on the dumbbell representation, we express DSI as a NN spin-ice model described by Hamiltonian H-0 perturbed by the Coulomb interactions among defects H-1. Then we apply LSA to H-0 and decompose the system into a mixture of loops and strings interacting via H-1. In simulation of the mixture, we employ the Metropolis algorithm. Our approach possesses two advantages: First, it is free of the so-called spin freezing problem; second, the computational cost for H-1 decreases exponentially with temperature, which can be viewed as an algorithmic realization of the projective equivalence concept. We compare numerical data with experimental results for Ho2Ti2O7 and Dy2Ti2O7 to demonstrate its predictability for these frustrated magnets.