Condensed Matter Theory

Abstract:

A three-dimensional Ising model with competing interactions up to third-neighbour layers is analysed using low-temperature series expansions and mean field theory. New sequences of phases springing from multiphase lines are found and the crossover to the behaviour of the ANNNI model is studied. Results are related to experimental findings on alloys, ferroelectrics, and polytypes. © 1985 The Institute of Physics.

Abstract:

A finite-size-scaling analysis is applied to two axial next-nearest- neighbor Ising (ANNNI) models. By using the scaling behavior of both the correlation length and the modulation wave vector we are able to clearly identify and distinguish between the ordered commensurate phases, the lock-in fluid phases, and in particular, the two types of incommensurate (floating) phases occurring in the models. As expected, the brickwork ANNNI model does not have a floating-solid phase, but instead has a q=(1/4) lock-in fluid phase above its 2 phase. On the basis of our results, we conclude that, in contrast to a recent suggestion, transfer-matrix methods can be a powerful tool in the study of two-dimensional models which exhibit incommensurate phases. © 1985 The American Physical Society.