Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

Abstract

Critical and in the highly frustrated regime also dynamical properties of the J1−J2 Ising model with competing nearest-neighbor J1 and second-nearest-neighbor J2 interactions on a honeycomb lattice are investigated by standard Monte Carlo and parallel tempering simulations. The phase boundary is determined as a function of the coupling ratio for the phase transition between the paramagnetic and ferromagnetic states within R≡J2/|J1|∈[−1/4,0]. It is confirmed that at least for R≥−0.2 the transition remains second-order and complies with the standard Ising universality class. In the highly frustrated regime of R<−0.2 and low temperatures the system tends to freeze to metastable domain states, separated by large energy barriers, which show extremely sluggish dynamics. The resulting huge equilibration and autocorrelation times hinder the analysis of critical properties and thus the character of the transition in this region remains to be determined.