Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Large-Sanalysis of a quantum axial next-nearest-neighbor Ising model in one dimension

Diptiman Sen

Published Mar 1, 1991• 7 citations
Publisher

Abstract

We study the large-S limit of a one-dimensional quantum spin model in a transverse magnetic field. For S=1/2, this is dual to the quantum Hamiltonian limit of the two-dimensional axial next-nearest-neighbor Ising model. The phase diagram has three regions; paramagnetic, ferromagnetic, and a modulated phase of period 2. The Peschel-Emery curve is discovered to be a disorder line. The long-distance correlation functions behave differently on the two sides of the line, and the correlation length goes to zero upon approaching it from either side.

DOI
10.1103/physrevb.43.5939

Related papers

Large-Sanalysis of one-dimensional quantum-spin models in a transverse magnetic field

Diptiman Sen, Bikas K. Chakrabarti

We analyze the zero-temperature phase diagram of two kinds of one-dimensional quantum-spin models in a transverse magnetic field. The first kind has uniform nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic couplings. A spin-wave analysis indicates the presence of several (possibly an infinite number of) commensurate modulated phases in the phase diagram. The three most prominent phases are paramagnetic, ferromagnetic, and a q=(1/4 phase of period four. The second kind of model is a spin-glass with only nearest-neighbor ferromagnetic interactions whose strengths are random and are characterized by a probability function. A classical large-S analysis shows the existence of a Griffiths phase lying in between a low-magnetic-field ferromagnetic phase and a high-magnetic-field paramagnetic phase. We present two order parameters that can together distinguish between the three phases.

Physical review. B, Condensed matter•Mar 1, 1990•7 citations

Density-matrix renormalization-group study of the disorder line in the quantum axial next-nearest-neighbor Ising model

Matteo Beccaria A, Massimo Campostrini B, Alessandra Feo

We apply density-matrix renormalization-group methods to study the phase diagram of the quantum axial next-nearest-neighbor Ising model in the region of low frustration where the ferromagnetic coupling is larger than the next-nearest-neighbor antiferromagnetic one. By finite-size scaling on lattices with up to 80 sites we locate precisely the transition line from the ferromagnetic phase to a paramagnetic phase without spatial modulation. We then measure and analyze the spin-spin correlation function in order to determine the disorder transition line where a modulation appears. We give strong numerical support to the conjecture that the Peschel-Emery one-dimensional line actually coincides with the disorder line. We also show that the critical exponent governing the vanishing of the modulation parameter at the disorder transition is ${\ensuremath{\beta}}_{q}=1∕2$.

arXiv:cond-mat/0511658•Physical Review B•Feb 7, 2006•50 citations

Hamiltonian limit of the two-dimensional axial next-nearest-neighbor Ising model: A many-body approach

Santiago D’Elía

The Hamiltonian limit of the two-dimensional axial next-nearest-neighbor Ising model is studied with use of an interacting-fermion technique. Details of the ferromagnetic side of the corresponding phase diagram are analyzed, especially the characterization of spatially modulated structures and the type of the phase transition.

Physical review. B, Condensed matter•Aug 1, 1992•1 citation

Quantum fidelity approach to the ground-state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field

O. F. de Alcantara Bonfim, B. Boechat, J. Florencio

In this work we analyze the ground-state properties of the s=1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field B_{x} and the strength of the next-nearest-neighbor interaction J_{2}, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and 〈2,2〉 phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second order, whereas the line between the floating and the 〈2,2〉 phases is possibly of first order.

arXiv:1705.09679•Physical review. E•Oct 17, 2017•10 citations

Quantum phase transitions in the one-dimensional transverse Ising model with second-neighbor interactions

P. R. C. Guimarães, J. A. Plascak, F. C. Sá Barreto +1 more

We apply a finite-size scaling approach to the one-dimensional spin-$1/2$ Ising model with nearest- and next-nearest-neighbor interactions in the presence of a transverse magnetic field. By using the scaling behavior of the energy gap we are able not only to determine the ferromagnetic-paramagnetic transition line at zero absolute temperature but also to compute the corresponding critical exponent. A comparison with other approaches is made, and aside for small discrepancies likely to occur at the thermodynamic limit, we believe that the present results are quite close to the unknown exact ones.

Physical review. B, Condensed matter•Aug 9, 2002•28 citations

Modulation of Local Magnetization in Two-Dimensional Axial-Next-Nearest-Neighbor Ising Model

René Derian, Andrej Gendiar, Tomotoshi Nishino

The axial next-nearest-neighbor Ising model is studied in two dimensions at finite temperature using the density matrix renormalization group. The model exhibits phase transition of the second-order between the antiphase in low temperature and the modulated phase in high temperature. Observing the domain wall free energy, we confirm that the modulation period in high-temperature side is well explained by the free-fermion picture.

arXiv:cond-mat/0605411•Journal of the Physical Society of Japan•Oct 25, 2006•12 citations
We study the large-S limit of a one-dimensional quantum spin model in a transverse magnetic field. For S=1/2, this is dual to the quantum Hamiltonian limit of the two-dimensional axial next-nearest-neighbor Ising model. The phase diagram has three regions; paramagnetic, ferromagnetic, and a modulated phase of period 2. The Peschel-Emery curve is discovered to be a disorder line. The long-distance correlation functions behave differently on the two sides of the line, and the correlation length goes to zero upon approaching it from either side.
We analyze the zero-temperature phase diagram of two kinds of one-dimensional quantum-spin models in a transverse magnetic field. The first kind has uniform nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic couplings. A spin-wave analysis indicates the presence of several (possibly an infinite number of) commensurate modulated phases in the phase diagram. The three most prominent phases are paramagnetic, ferromagnetic, and a q=(1/4 phase of period four. The second kind of model is a spin-glass with only nearest-neighbor ferromagnetic interactions whose strengths are random and are characterized by a probability function. A classical large-S analysis shows the existence of a Griffiths phase lying in between a low-magnetic-field ferromagnetic phase and a high-magnetic-field paramagnetic phase. We present two order parameters that can together distinguish between the three phases.
We apply density-matrix renormalization-group methods to study the phase diagram of the quantum axial next-nearest-neighbor Ising model in the region of low frustration where the ferromagnetic coupling is larger than the next-nearest-neighbor antiferromagnetic one. By finite-size scaling on lattices with up to 80 sites we locate precisely the transition line from the ferromagnetic phase to a paramagnetic phase without spatial modulation. We then measure and analyze the spin-spin correlation function in order to determine the disorder transition line where a modulation appears. We give strong numerical support to the conjecture that the Peschel-Emery one-dimensional line actually coincides with the disorder line. We also show that the critical exponent governing the vanishing of the modulation parameter at the disorder transition is ${\ensuremath{\beta}}_{q}=1∕2$.
In this work we analyze the ground-state properties of the s=1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field B_{x} and the strength of the next-nearest-neighbor interaction J_{2}, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and 〈2,2〉 phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second order, whereas the line between the floating and the 〈2,2〉 phases is possibly of first order.
We apply a finite-size scaling approach to the one-dimensional spin-1/21/21/2 Ising model with nearest- and next-nearest-neighbor interactions in the presence of a transverse magnetic field. By using the scaling behavior of the energy gap we are able not only to determine the ferromagnetic-paramagnetic transition line at zero absolute temperature but also to compute the corresponding critical exponent. A comparison with other approaches is made, and aside for small discrepancies likely to occur at the thermodynamic limit, we believe that the present results are quite close to the unknown exact ones.