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Physical Review A

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

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

Published Dec 1, 1971• 186 citations
Publisher

Abstract

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

DOI
10.1103/physreva.4.2331

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Computer calculations of the time-dependent spin and energy correlation functions of the classical one-dimensional $\mathrm{XY}$ model at infinite temperature are reported. Plots of $〈{S}_{z}^{i}{S}_{z}^{i}(t)〉$, $〈{S}_{z}^{i}{S}_{z}^{i+1}(t)〉$, $〈{\ensuremath{\epsilon}}^{i}{\ensuremath{\epsilon}}^{i}(t)〉$, and $(\frac{1}{2})[〈{S}_{x}^{i}{S}_{x}^{i}(t)〉+〈{S}_{y}^{i}{S}_{y}^{i}(t)〉]$ out to times $Jt=9$ are given (${\ensuremath{\epsilon}}^{i}$ is the energy-density operator and $\ensuremath{\hbar}J$ is the exchange integral). Comparison is made with the exact results for the spin-1/2 $\mathrm{XY}$ model. After an appropriate scaling of the exchange integral and normalization to the classical value at $t=0$ the values of the spin-1/2 functions are close to the values of their classical counterparts for times up to $\mathrm{Jt}\ensuremath{\approx}4$.

Physical review. B, Solid state•Oct 1, 1974•9 citations
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
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.
Computer calculations of the time-dependent spin and energy correlation functions of the classical one-dimensional XY\mathrm{XY}XY model at infinite temperature are reported. Plots of 〈SziSzi(t)〉〈{S}_{z}^{i}{S}_{z}^{i}(t)〉〈Szi​Szi​(t)〉, 〈SziSzi+1(t)〉〈{S}_{z}^{i}{S}_{z}^{i+1}(t)〉〈Szi​Szi+1​(t)〉, $〈{\ensuremath{\epsilon}}^{i}{\ensuremath{\epsilon}}^{i}(t)〉$, and (12)[〈SxiSxi(t)〉+〈SyiSyi(t)〉](\frac{1}{2})[〈{S}_{x}^{i}{S}_{x}^{i}(t)〉+〈{S}_{y}^{i}{S}_{y}^{i}(t)〉](21​)[〈Sxi​Sxi​(t)〉+〈Syi​Syi​(t)〉] out to times Jt=9Jt=9Jt=9 are given (${\ensuremath{\epsilon}}^{i}$ is the energy-density operator and $\ensuremath{\hbar}J$ is the exchange integral). Comparison is made with the exact results for the spin-1/2 XY\mathrm{XY}XY model. After an appropriate scaling of the exchange integral and normalization to the classical value at t=0t=0t=0 the values of the spin-1/2 functions are close to the values of their classical counterparts for times up to $\mathrm{Jt}\ensuremath{\approx}4$.