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We study a classical fully-frustrated honeycomb lattice Ising model usingMarkov chain Monte Carlo methods and exact calculations . The Hamiltonianrealizes a degenerate ground state manifold of equal-energy states, where eachhexagonal plaquette of the lattice has one and only one frustrated bond, withan extensive residual entropy that grows as the number of spins N. Traditionalsingle-spin flip Monte Carlo methods fail to sample all possible spinconfigurations in this ground state efficiently, due to their separation bylarge energy barriers. We develop a non-local "chain-flip" algorithm thatsolves this problem, and demonstrate its effectiveness on the Ising Hamiltonianwith and without perturbative interactions. The two perturbations consideredare 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 groundstate. In the case of the magnetic field, two magnetized ground states withnon-extensive entropy are found, and two special values of h exist where theresidual entropy again becomes extensive, scaling proportional to N ln phi,where phi is the golden ratio.

Monte Carlo study of degenerate groundstates and residual entropy in a frustrated honeycomb lattice Ising model