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 A

Statistical Mechanics of the XY Model. II. Spin-Correlation Functions

Eytan Barouch, Barry M. McCoy

Published Feb 1, 1971• 830 citations
Publisher

Abstract

The spin-correlation functions of the one-dimensional $XY$ model are studied in the presence of a constant magnetic field. We find that the asymptotic behavior of these correlation functions depends strongly on the various parameters of the Hamiltonian.

DOI
10.1103/physreva.3.786

Related papers

Statistical Mechanics of the XY Model. IV. Time-Dependent Spin-Correlation Functions

Barry M. McCoy, Eytan Barouch, Douglas B. Abraham

We compute the correlation functions 〈S0x(t)SRx(0)〉 and 〈S0y(t)SRy(0)〉 at T=0 for the one-dimensional XY model in the presence of a magnetic field.Received 2 June 1971DOI:https://doi.org/10.1103/PhysRevA.4.2331©1971 American Physical Society

Physical Review A•Dec 1, 1971•186 citations

Statistical Mechanics of the XY Model. III

Eytan Barouch, Barry M. McCoy

We continue the considerations of the first paper in this series by studying the time dependence of the spin-correlation functions in response to a step-function change in the external magnetic field. We find that these correlation functions exhibit nonergodic behavior.

Physical Review A•Jun 1, 1971•150 citations

Quantum critical properties of non-Hermitian XY models with magnetic field

Jia-Jia Luo, Volker Meden

The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.

quant-pharXiv:2606.07275•Jun 8, 2026•0 citations

Transverse spin correlation function of the one-dimensional spin- XY model in a longitudinal magnetic field

Takashi Tonegawa

Journal of Magnetism and Magnetic Materials•Feb 1, 1983•0 citations

THERE IS LIFE IN THE OLD HORSE YET OR WHAT ELSE WE CAN LEARN STUDYING SPIN-1/2 XY CHAINS

Derzhko

We review some recent results on statistical mechanics of the one-dimensional spin-1/2 XY systems paying special attention to the dynamic and thermodynamic properties of the models with Dzyaloshinskii-Moriya interaction, correlated disorder, and regularly alternating Hamiltonian parameters.

Condensed Matter Physics•Jan 1, 2002•4 citations

There is life in the old horse yet or what else we can learn studying spin-1/2 XY chains

Oleg Derzhko

We review some recent results on statistical mechanics of the one-dimensional spin-1/2 XY systems paying special attention to the dynamic and thermodynamic properties of the models with Dzyaloshinskii-Moriya interaction, correlated disorder, and regularly alternating Hamiltonian parameters.

arXiv:cond-mat/0304344•Apr 15, 2003•0 citations
The spin-correlation functions of the one-dimensional XYXYXY model are studied in the presence of a constant magnetic field. We find that the asymptotic behavior of these correlation functions depends strongly on the various parameters of the Hamiltonian.
The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.