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 $(P)\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}2$ 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 $P\ensuremath{-}C$ and $I\ensuremath{-}C$ transitions are of first order whereas the $P\ensuremath{-}I$ transition seems to be of second order. The model is used to interpret the $P\ensuremath{-}I\ensuremath{-}C$ transitions in $\ensuremath{\beta}$-eucryptite.