Frustrated Ising model on the honeycomb lattice: Metastability and universality

Abstract

We study the Ising model with competing ferromagnetic nearest- and antiferromagnetic next-nearest-neighbor interactions of strengths $J_1 > 0$ and $J_2 < 0$, respectively, on the honeycomb lattice. For $J_2 > - J_1 / 4$ it has a ferromagnetic ground state, and previous work has shown that at least for $J_2 \gtrsim -0.2 J_1$ the transition is in the Ising universality class. For even lower $J_2$ some indicators pointing towards a first-order transition were reported. By utilizing population annealing Monte Carlo simulations together with a rejection-free and adaptive update, we can equilibrate systems with $J_2$ as low as $-0.23 J_1$. By means of a finite-size scaling analysis we show that the system undergoes a second-order phase transition within the Ising universality class at least down to $J_2 =-0.23 J_1$ and, most likely, for all $J_2 > - J_1 / 4$. As we show here, there exist very long-lived metastable states in this system explaining the first-order like behavior seen in only partially equilibrated systems.