Residual entropy, bicriticality, and tricriticality in the frustrated Ising model on the honeycomb lattice

Phase transitions and thermodynamic properties of the frustrated J 1- J 2- J 3 Ising model on the honeycomb lattice are investigated by using the cluster mean-field theory and Monte Carlo simulations. We investigate the role of thermal fluctuations in the model with ferromagnetic exchange interactions between first and third neighbors and antiferromagnetic second-neighbor couplings. Our findings indicate that these competing interactions can lead to three forms of long-range order and different scenarios concerning phase transitions. For weak third-neighbor interactions, strong frustration effects bring the ordering temperature to absolute zero and lead to residual entropy. Moreover, thermodynamic signatures of frustration such as a round maximum in the specific heat can be found above the ordering temperature. The model also exhibits continuous and discontinuous order-disorder phase transitions, hosting tricriticality for weak and moderate strengths of thirdneighbor couplings. At strong enough third-neighbor couplings, discontinuous order-disorder phase transitions are suppressed and a bicritical point can be observed. Our findings are discussed in connection with recent experimental results for Ising spin systems on the frustrated honeycomb lattice, including van der Waals magnets.