2 × 2 commensurate-incommensurate transition in Ising models: Monte Carlo simulation

Abstract

Phase diagrams of Ising models with antiferromagnetic nearest-(NN) and next-nearest-neighbor (NNN) interactions are obtained by Monte Carlo simulations. For the triangular lattice a paramagnetic $\mathrm{}\left(P\right)\mathrm{}-2\times 2$ commensurate ($C$) phase transition is found, which is second order when the NN interaction is small. The exponents are consistent with the ones of the four-state Potts model. For large NNN interactions the transition becomes first order. For three-dimensional stacking of triangular layers an incommensurate ($I$) phase is found in addition. The $P-C$ and $I-C$ transitions are of first order whereas the $P-I$ transition seems to be of second order. The model is used to interpret the $P-I-C$ transitions in $\beta$-eucryptite.