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

Two-dimensional axial third-nearest-neighbor Ising model and theS=1/2 anisotropic Heisenberg chain

Marcelo D. Grynberg, Horacio Ceva

Published Jun 1, 1991• 0 citations
Publisher

Abstract

We consider an axial Ising model with competing interactions up to third neighbors within a low-temperature approximation in terms of interacting and nonreversing domain walls. Assuming small third-neighbor coupling, we find a close relation between the transfer matrix of this classical model and the Hamiltonian of an S=1/2 anisotropic Heisenberg chain in a uniform magnetic field. This connection allows us to obtain the phase boundaries of the ferromagnetic and other low-temperature modulated states. The ground-state energy for arbitrary magnetization values of the Heisenberg chain is shown to provide information about the density of walls or wave number. In contrast with the two-dimensional axial next-nearest-neighbor Ising model, this quantity displays plateaus and reentrant behavior for some relations among the coupling constants. An alternative way to evaluate correlation functions in the antiferromagnetic Heisenberg chain is presented.

DOI
10.1103/physrevb.43.13506

Related papers

Interacting-walls approximation in the two-dimensional axial third-nearest-neighbor Ising model

Marcelo D. Grynberg, Horacio Ceva

The two-dimensional axial Ising model with competing interactions up to third neighbors is studied by analytical methods. A low-temperature approximation is used to describe the system as a sequence of interacting and nonreversing domain walls for small values of the third-neighbor interaction. The boundaries of the ferromagnetic and other low-temperature modulated phases are obtained by means of the ground-state energy of the Heisenberg-Ising chain after reducing the problem to a system of spinless interacting fermions in one dimension. The density of walls or wave number obtained within this approximation results to be continuously varying and for some relations among the coupling constants it displays plateaus and re-entrant phenomena.

Physical review. B, Condensed matter•Jan 1, 1990•3 citations

Ground-State Properties of the One-Dimensional Anisotropic Spin-1/2 Heisenberg Magnet with Competing Interactions

Takashi Tonegawa, I. Harada, J.-i. Igarashi

Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fiuid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.

Progress of Theoretical Physics Supplement•May 16, 2013•2 citations

Interacting-fermion approximation in the two-dimensional axial next-nearest-neighbor Ising model

Marcelo D. Grynberg, Horacio Ceva

We investigate the effect of including doman-wall interactions in the two-dimensional axial next-nearest-neighbor Ising model. At low temperatures this problem is reduced to a one-dimensional system of interacting fermions which can be treated exactly. It is found that the critical boundaries of the low-temperature phases are in good agreement with those obtained using a free-fermion approximation. In contrast with the monotonic behavior derived from the free-fermion approach, the wall density or wave number displays reentrant phenomena when the ratio of the next-nearest-neighbor and nearest-neighbor interactions is greater than 1/2.

Physical review. B, Condensed matter•Jun 1, 1991•4 citations

One-Dimensional Isotropic Spin-1/2 Heisenberg Magnet with Ferromagnetic Nearest-Neighbor and Antiferromagnetic Next-Nearest-Neighbor Interactions

Takashi Tonegawa, Isao Harada

We study the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions which compete with each other. Extrapolating the exact results for finite-size systems of up to 20 spins, we estimate the ground-state energy and the ground-state two-spin correlation function in the infinite-size limit. Using the cluster transfer matrix method, we also calculate the temperature dependence of the internal energy and the specific heat and that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the two-spin correlation function in the long-distance limit is characterized. We compare the results of these calculations with those obtained previously for the case where the nearest-neighbor interaction is antiferromagnetic.

Journal of the Physical Society of Japan•Aug 15, 1989•64 citations

Ground-State Properties of the One-Dimensional Anisotropic Spin-1/2 Heisenberg Magnet with Competing Interactions

Takashi Tonegawa, Isao Harada, Jun-ichi Igarashi

Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisen­ berg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest­ neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fluid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.

Progress of Theoretical Physics Supplement•Jan 1, 1990•22 citations

Finite-size study of a spin-1/2 Heisenberg chain with competing interactions: Phase diagram and critical behavior

K. Hallberg, Eduardo R. Gagliano, C. A. Balseiro

We study the ground-state properties of the one-dimensional anisotropic spin-1/2 antiferromagnetic Heisenberg model with competing antiferromagnetic second-neighbor Ising interaction. Using the modified Lanczos method, we obtain the phase diagram in parameter space and different correlation functions, which we use to characterize the different phases. For small next-nearest-neighbor parameters we evaluate the critical exponent \ensuremath{\eta} of the spin-spin correlation function. We find good agreement between the numerical results and those obtained using the Luther and Peschel approach.

Physical review. B, Condensed matter•May 1, 1990•23 citations
We consider an axial Ising model with competing interactions up to third neighbors within a low-temperature approximation in terms of interacting and nonreversing domain walls. Assuming small third-neighbor coupling, we find a close relation between the transfer matrix of this classical model and the Hamiltonian of an S=1/2 anisotropic Heisenberg chain in a uniform magnetic field. This connection allows us to obtain the phase boundaries of the ferromagnetic and other low-temperature modulated states. The ground-state energy for arbitrary magnetization values of the Heisenberg chain is shown to provide information about the density of walls or wave number. In contrast with the two-dimensional axial next-nearest-neighbor Ising model, this quantity displays plateaus and reentrant behavior for some relations among the coupling constants. An alternative way to evaluate correlation functions in the antiferromagnetic Heisenberg chain is presented.
The two-dimensional axial Ising model with competing interactions up to third neighbors is studied by analytical methods. A low-temperature approximation is used to describe the system as a sequence of interacting and nonreversing domain walls for small values of the third-neighbor interaction. The boundaries of the ferromagnetic and other low-temperature modulated phases are obtained by means of the ground-state energy of the Heisenberg-Ising chain after reducing the problem to a system of spinless interacting fermions in one dimension. The density of walls or wave number obtained within this approximation results to be continuously varying and for some relations among the coupling constants it displays plateaus and re-entrant phenomena.
Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fiuid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.
We investigate the effect of including doman-wall interactions in the two-dimensional axial next-nearest-neighbor Ising model. At low temperatures this problem is reduced to a one-dimensional system of interacting fermions which can be treated exactly. It is found that the critical boundaries of the low-temperature phases are in good agreement with those obtained using a free-fermion approximation. In contrast with the monotonic behavior derived from the free-fermion approach, the wall density or wave number displays reentrant phenomena when the ratio of the next-nearest-neighbor and nearest-neighbor interactions is greater than 1/2.
We study the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions which compete with each other. Extrapolating the exact results for finite-size systems of up to 20 spins, we estimate the ground-state energy and the ground-state two-spin correlation function in the infinite-size limit. Using the cluster transfer matrix method, we also calculate the temperature dependence of the internal energy and the specific heat and that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the two-spin correlation function in the long-distance limit is characterized. We compare the results of these calculations with those obtained previously for the case where the nearest-neighbor interaction is antiferromagnetic.
Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisen­ berg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest­ neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fluid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.
We study the ground-state properties of the one-dimensional anisotropic spin-1/2 antiferromagnetic Heisenberg model with competing antiferromagnetic second-neighbor Ising interaction. Using the modified Lanczos method, we obtain the phase diagram in parameter space and different correlation functions, which we use to characterize the different phases. For small next-nearest-neighbor parameters we evaluate the critical exponent \ensuremath{\eta} of the spin-spin correlation function. We find good agreement between the numerical results and those obtained using the Luther and Peschel approach.