frustrated honeycomb lattice Ising model

We study a classical fully-frustrated honeycomb lattice Ising model using Markov chain Monte Carlo methods and exact calculations . The Hamiltonian realizes a degenerate ground state manifold of equal-energy states, where each hexagonal plaquette of the lattice has one and only one unsatisfied bond, with an extensive residual entropy that grows as the number of spins N . Traditional singlespin flip Monte Carlo methods fail to sample all possible spin configurations in this ground state efficiently, due to their separation by large energy barriers. We develop a non-local “chain-flip” algorithm that solves this problem, and demonstrate its effectiveness on the Ising Hamiltonian with and without perturbative interactions. The two perturbations considered are a slightly weakened bond, and an external magnetic field h. For some cases, the chain-flip move is necessary for the simulation to find an ordered ground state. In the case of the magnetic field, two magnetized ground states with non-extensive entropy are found, and two special values of h exist where the residual entropy again becomes extensive, scaling proportional to N lnφ, where φ is the golden ratio.