Rejection-Free Population Annealing and Frustrated Ising Models

Population annealing (PA) is a sequential Monte Carlo technique suited for massively parallel simulations of systems with sampling diffiulties. While simulating a population of system copies, population control allows the algorithm to amplify well equilibrated copies while getting rid of lesss well adapted ones and hence speed up the overall relaxation process. While this works well for systems with many competing states, it does nothing to speed up sampling in cases where the embedded conventional Markov chain Monte Carlo dynamics is slow due to small acceptance rates, such as for simulations at low temperatures. We show here that a combination of rejection-free or event-driven simulation algorithms such as the n-fold way with the meta-heuristic provided by population annealing allows to successfully tackle problems where low acceptance rates would otherwise make a standard PA simulation inefficient. The method is used to study the behavior of a frustrated Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor interactions of strength $J_1$ and antiferromagnetic next-nearest-neighbor interactions of strength $J_2$ close to the special point $J_2 = -J_1/4$. While conventional methods seemed to indicate slowing-down effects reminiscent of a first-order phase transition, these are found to be artifacts of the transition temperature approaching zero and the accompanying Metropolis acceptance rates disappearing. In contrast, rejection-free PA allows to study this problem in detail and map out the phase diagram.