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Journal of Physics A Mathematical and General

A quantum Hamiltonian approach to the two-dimensional axial next-nearest-neighbour Ising model

Michael N. Barber, Phillip M. Duxbury

Published Jul 1, 1981• 121 citations
Publisher

Abstract

A quantum Hamiltonian analogue of the two-dimensional axial next-nearest-neighbour Ising (ANNNI) model is presented. The phase diagram is investigated by the analysis of perturbation series and by finite-lattice methods.
DOI
10.1088/0305-4470/14/7/006

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Hamiltonian studies of the two-dimensional axial next-nearest neighbour Ising (ANNNI) model. II. Finite-lattice mass gap calculations

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The quantum Hamiltonian analogue of the two-dimensional ANNNI model is investigated by finite-lattice mass gap methods. By using lattice sizes capable of simulating systems of varying modulation, the authors are able to show the existence of a modulated phase between the paramagnetic and (2,2) antiphase regions. The modulation on the incommensurate to paramagnetic boundary is shown to vary and this variation is calculated as a function of the anisotropy. In addition, they find evidence for an XY-like transition from the incommensurate to the paramagnetic phase and perhaps a non-universal transition from the paramagnetic phase to the antiphase.

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Hamiltonian studies of the two-dimensional axial next-nearest neighbour Ising (ANNNI) model: II. Finite-lattice mass gap calculations

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A two-leg quantum Ising ladder: a bosonization study of the ANNNI model

D Allen, P. Azaria, P. Lecheminant

The quantum axial next-to-nearest neighbour Ising (ANNNI) chain in a transverse field is investigated by means of the bosonization approach in the limit of the large next-to-nearest neighbour interaction. In this regime, this model can be viewed as a weakly coupled two-leg zigzag ladder which enables us to derive its low-energy effective field theory. In particular, it is shown that the effect of frustration in the system is captured by the presence of a non-zero conformal spin perturbation that accounts for the existence of all the incommensurate phases of the model.

arXiv:cond-mat/0101404•Journal of Physics A Mathematical and General•May 18, 2001•42 citations
The quantum Hamiltonian analogue of the two-dimensional ANNNI model is investigated by finite-lattice mass gap methods. By using lattice sizes capable of simulating systems of varying modulation, the authors are able to show the existence of a modulated phase between the paramagnetic and (2,2) antiphase regions. The modulation on the incommensurate to paramagnetic boundary is shown to vary and this variation is calculated as a function of the anisotropy. In addition, they find evidence for an XY-like transition from the incommensurate to the paramagnetic phase and perhaps a non-universal transition from the paramagnetic phase to the antiphase.
The quantum axial next-to-nearest neighbour Ising (ANNNI) chain in a transverse field is investigated by means of the bosonization approach in the limit of the large next-to-nearest neighbour interaction. In this regime, this model can be viewed as a weakly coupled two-leg zigzag ladder which enables us to derive its low-energy effective field theory. In particular, it is shown that the effect of frustration in the system is captured by the presence of a non-zero conformal spin perturbation that accounts for the existence of all the incommensurate phases of the model.