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Journal of Applied Physics

Wave-vector-dependent spectra of quantum systems with competing interactions

M. Kolb, K. A. Penson

Published Apr 15, 1985• 1 citation
Publisher

Abstract

The analysis of phase diagrams of one-dimensional quantum versions of axial next-nearest-neighbor Ising (ANNNI) and competing two- and four-spin interaction models in two dimensions was made. The zero-temperature wave-vector-dependent spectra for finite chains with up to L≤16 spins indicate a qualitative difference between the two models: while the existence of an incommensurate phase is confirmed for the ANNNI case, our results do not suggest that such a phase exists in the two- and four-spin model.

DOI
10.1063/1.335136

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PRSM•Aug 7, 2015•1 citation
The analysis of phase diagrams of one-dimensional quantum versions of axial next-nearest-neighbor Ising (ANNNI) and competing two- and four-spin interaction models in two dimensions was made. The zero-temperature wave-vector-dependent spectra for finite chains with up to L≤16 spins indicate a qualitative difference between the two models: while the existence of an incommensurate phase is confirmed for the ANNNI case, our results do not suggest that such a phase exists in the two- and four-spin model.
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.
The mean-field phase diagram of a three-dimensional axial-next-nearest-neighbor Ising (ANNNI) model in a transverse field has been studied here. The dynamical modes are found by using the random-phase approximation and the phase diagram is also obtained from the softening condition of these modes. For a one-dimensional ANNNI model in a transverse field, these dynamical modes are obtained here more accurately using a Jordan-Wigner-type transformation (with some approximations). Softening of these modes gives the zero-temperature phase diagram in one dimension.
The authors study in detail the short-range order at low temperature in a one-dimensional Ising model with competing interactions by studying various staggered susceptibilities. From this they get a 'phase diagram' which divides regions of various dominant short-range orders. This phase diagram is shown to resemble qualitatively the low-temperature phase diagram of the anisotropic next-nearest-neighbour interaction Ising (ANNNI) model in higher dimensions. They argue that this method of studying a corresponding one-dimensional problem may be useful to understand the phase structure of complex higher-dimensional systems.
The phase diagrams of the ferromagnetic two-dimensional mixed spin-1 and spin-1/2 Ising model with four-spin interaction J4 and next-nearest couplings J’ are investigated by the use of the finite cluster approximation based on single-site cluster theory. The state equations are derived for the two-dimensional square lattice. The phase diagram is qualitatively and quantitatively different from that obtained when the interaction J’ is ignored. In fact, the system exhibits a variety of interesting features resulting from the introduction of the next-nearest neighbor interaction (NNN). It undergoes two kinds of behavior according to the negative and the positive value of J’. In particular, for J4/J2=-4, the system keeps the coexistence of the two ground state up to J’-dependent finite temperature.