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

Acta Physica Sinica

A TRANSVERSE XY MODEL WITH NEXT NEAREST NEIGHBOUR INTERACTIONS

Xu Bo-wei, TANG KUN-FA, 上海交通大学物理系

Published Jan 1, 1989• 2 citations
Publisher

Abstract

We generalize the transverse XY model to the case with NNN interactions. The Hamiltonian is H=g∑nσn2-∑n ((1+γ)/2σnxσn+1x+(1-γ)/2σnyσn+1y)-λ∑n ((1+β)/2σnxσn+2x+(1-β)/2σnyσn+2y). It is shown that the model with β=0 and γ≠0 isequivalent to the free fermion field in the vicinity of critical point, so that it belongs to the Ising universality class.

DOI
10.7498/aps.38.645

Related papers

Critical behaviour of a model with NNN interaction

Wei Fan, Bo-Wei Xu

A one-dimensional quantum model with next-nearest-neighbour interaction is studied. Under the long-wavelength approximation, the authors predict that this model belongs to the same universality class as the Ising model. This conclusion is checked with a numerical solution which is consistent with the prediction in both critical point and critical exponent.

Journal of Physics A Mathematical and General•Sep 7, 1990•9 citations

Critical Behavior of an NNN Interaction Model

Hai-Yan Zhang, Bo-Wei Xu

A one-dimensional quantum mode1 with generalized next-nearest neighbour interaction is studied. The numerical results convince us of the existence of critical phenomenon in this model. The critical point condition is given, and the model belongs to the Ising universality.

Communications in Theoretical Physics•Jul 1, 1992•0 citations

Ising-like phase transition in the square lattice fully frustrated XY model with nearest next neighbor couplings

Ren Qing

The Isinglike phase transition in the square lattice fully frustrated XY model with nearest next neighbor (NNN) couplings is studied using the finitesize scaling theory. The critical temperature Tc and static critical exponents 2β/ν and ν are determined. When the NNN coupling variable x=0.5, it is found that in the model exists Isinglike phase transition with the critical temperature Tc=0.404 3±0.000 5 and ν= 0.80±0.05.

Journal of Zhejiang University(Sciences Edition)•Jan 1, 2003•0 citations

Non-universality in the Ising model with nearest and next-nearest neighbour interactions

Michael N. Barber

The critical behaviour of the Ising model on the square lattice with ferromagnetic nearest-neighbour interactions (J) and anti-ferromagnetic next-nearest neighbour interactions (J') is discussed for small lambda =J/ mod J' mod . The singular part of the free energy is calculated to second order in lambda by perturbation theory. Near the critical temperature of the unperturbed system (J=0), this expansion is found to have a form which may be exponentiated yielding, for non-zero lambda , a non-universal critical line along which the exponents vary continuously with lambda . For small lambda , the specific heat exponent, alpha = alpha 1 lambda 2 +O( lambda 2 ) with alpha 1 approximately=1.5.

Journal of Physics A Mathematical and General•May 1, 1979•51 citations

The Ising model with a transverse field. II. Ground state properties

Pierre M. Pfeuty, Roger James Elliott

For Pt. I see ibid., vol. 4, 2359 (1971). The properties of the Ising model with a transverse field, with the Hamiltonian written H=- Gamma Sigma i S i x - 1 / 2 Sigma i,j J ij S i z S j z , are studied by perturbation expansions at T=0 in the ground state, both below and above the critical field Gamma C , for an hypercubic lattice and short range interactions. The order parameter (S z ) and the correlation function G=) Sigma i S i z Sigma j S j z ) are calculated respectively below and above Gamma C . The gap in the excitation spectrum is also studied above the critical field. The critical behaviour obtained from these expansions at T=0 is different from that obtained at T finite and is shown to be analogous to the critical behaviour of the Ising model for a lattice with one more dimension.

Journal of Physics C Solid State Physics•Oct 28, 1971•214 citations

The XY Model with Nearest and Next‐Nearest Neighbour Interaction in a Transverse Field

O. N. Borges, L. A. Amarante Ribeiro, L. L. Gonçlalves

Abstract The one‐dimensional XY model in a transverse field with first and second neighbour interactions is discussed, in the framework of the spectral density method, and in a first order approximation. The ground state is studied in detail and the phase transitions induced by the transverse field are determined. The phase diagram is obtained and it is shown that it presents a bicritical point.

physica status solidi (b)•Oct 1, 1984•0 citations
We generalize the transverse XY model to the case with NNN interactions. The Hamiltonian is H=g∑nσn2-∑n ((1+γ)/2σnxσn+1x+(1-γ)/2σnyσn+1y)-λ∑n ((1+β)/2σnxσn+2x+(1-β)/2σnyσn+2y). It is shown that the model with β=0 and γ≠0 isequivalent to the free fermion field in the vicinity of critical point, so that it belongs to the Ising universality class.
The critical behaviour of the Ising model on the square lattice with ferromagnetic nearest-neighbour interactions (J) and anti-ferromagnetic next-nearest neighbour interactions (J') is discussed for small lambda =J/ mod J' mod . The singular part of the free energy is calculated to second order in lambda by perturbation theory. Near the critical temperature of the unperturbed system (J=0), this expansion is found to have a form which may be exponentiated yielding, for non-zero lambda , a non-universal critical line along which the exponents vary continuously with lambda . For small lambda , the specific heat exponent, alpha = alpha 1 lambda 2 +O( lambda 2 ) with alpha 1 approximately=1.5.
For Pt. I see ibid., vol. 4, 2359 (1971). The properties of the Ising model with a transverse field, with the Hamiltonian written H=- Gamma Sigma i S i x - 1 / 2 Sigma i,j J ij S i z S j z , are studied by perturbation expansions at T=0 in the ground state, both below and above the critical field Gamma C , for an hypercubic lattice and short range interactions. The order parameter (S z ) and the correlation function G=) Sigma i S i z Sigma j S j z ) are calculated respectively below and above Gamma C . The gap in the excitation spectrum is also studied above the critical field. The critical behaviour obtained from these expansions at T=0 is different from that obtained at T finite and is shown to be analogous to the critical behaviour of the Ising model for a lattice with one more dimension.