Abstract
The phase diagrams of the one-dimensional quantum versions of the two-dimensional axial next-nearest-neighbor Ising (ANNNI) and the competing two-plus-four spin-interaction models are compared. The analysis of the zero-temperature wave-vector-dependent spectrum indicates a qualitative difference between the two models: while our finite-chain results support the existence of an incommensurate phase for the ANNNI case, they suggest that there is no such phase in the two-plus-four spin case.
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