Journal of Statistical Physics

Excluded Volume Effects for Frequency Moments of the Spin Autocorrelation Function of the Heisenberg Model on a Square Lattice at High Temperatures

V. E. Zobov, Michael Alekseevich Popov

Published Nov 1, 1999• 6 citations

Publisher

DOI: 10.1023/a:1004675527713

Related papers

High-temperature dynamics of the anisotropic spin-1/2 square lattice Heisenberg model studied by moment methods

Joachim Stolze, U. Brandt

The European Physical Journal BFeb 1, 19894 citations

Temperature and field dependence of autocorrelation functions for the one-dimensional Heisenberg antiferromagnet

Gerhard H. Muller, H. Beck

Journal of Magnetism and Magnetic MaterialsJan 1, 19801 citation

Spectral signature of quantum spin diffusion in dimensionsd=1, 2, and 3

Markus Böhm, Hajo Leschke, M Henneke +3 more

Physical review. B, Condensed matterJan 1, 199419 citations

High-frequency asymptotics of the autocorrelation function in the Heisenberg paramagnet

V. E. Zobov

Physics Letters ADec 1, 19867 citations

Time-dependent autocorrelation function for a linear Heisenberg chain at infinite temperature

Amit Sur, Irving J. Lowe

Physical review. B, Solid stateMar 1, 197528 citations

Autocorrelation function of the Heisenberg ferromagnet at elevated temperatures

T. Morita, Katsushi Kobayashi, Seiichiro Katsura +1 more

Physics Letters AAug 1, 19709 citations

Journal of Statistical Physics

Excluded Volume Effects for Frequency Moments of the Spin Autocorrelation Function of the Heisenberg Model on a Square Lattice at High Temperatures

V. E. Zobov, Michael Alekseevich Popov

Published Nov 1, 1999• 6 citations

Publisher

DOI: 10.1023/a:1004675527713

Related papers

High-temperature dynamics of the anisotropic spin-1/2 square lattice Heisenberg model studied by moment methods

Joachim Stolze, U. Brandt

The European Physical Journal BFeb 1, 19894 citations

Temperature and field dependence of autocorrelation functions for the one-dimensional Heisenberg antiferromagnet

Gerhard H. Muller, H. Beck

Journal of Magnetism and Magnetic MaterialsJan 1, 19801 citation

Spectral signature of quantum spin diffusion in dimensionsd=1, 2, and 3

Markus Böhm, Hajo Leschke, M Henneke +3 more

The spectral densities of dynamical spin autocorrelation functions at infinite temperature are studied for the S=1/2XXZ model (with exchange couplings ${\mathit{J}}_{\mathit{x}}$ = ${\mathit{J}}_{\mathit{y}}$ \ensuremath{\equiv}J, ${\mathit{J}}_{\mathit{z}}$ ) on the linear chain, the square lattice, and the simple cubic lattice. The low-frequency behavior of a given spectral density is inferred from certain characteristic properties of its continued-fraction coefficients as determined from computed frequency moments. The analysis yields estimates for the ${\mathit{J}}_{\mathit{z}}$ /J dependence of the infrared-singularity exponent. In the d=1 case, the exponent for spin fluctuations perpendicular to the O(2) symmetry axis responds sensitively as the anisotropy parameter sweeps across the O(3) symmetry point ${\mathit{J}}_{\mathit{z}}$ /J=1, while the exponent for the parallel fluctuations shows little variation. In the cases d=2 and d=3 the same observations are made for autocorrelation functions of aggregate spins in chains and lattice planes, respectively.The spectral densities of dynamical spin autocorrelation functions at infinite temperature are studied for the S=1/2XXZ model (with exchange couplings ${\mathit{J}}_{\mathit{x}}$=${\mathit{J}}_{\mathit{y}}$\ensuremath{\equiv}J,${\mathit{J}}_{\mathit{z}}$) on the linear chain, the square lattice, and the simple cubic lattice. The low-frequency behavior of a given spectral density is inferred from certain characteristic properties of its continued-fraction coefficients as determined from computed frequency moments. The analysis yields estimates for the ${\mathit{J}}_{\mathit{z}}$/J dependence of the infrared-singularity exponent. In the d=1 case, the exponent for spin fluctuations perpendicular to the O(2) symmetry axis responds sensitively as the anisotropy parameter sweeps across the O(3) symmetry point ${\mathit{J}}_{\mathit{z}}$/J=1, while the exponent for the parallel fluctuations shows little variation. In the cases d=2 and d=3 the same observations are made for autocorrelation functions of aggregate spins in chains and lattice planes, respectively.

Physical review. B, Condensed matterJan 1, 199419 citations

High-frequency asymptotics of the autocorrelation function in the Heisenberg paramagnet

V. E. Zobov

Physics Letters ADec 1, 19867 citations

Time-dependent autocorrelation function for a linear Heisenberg chain at infinite temperature

Amit Sur, Irving J. Lowe

Numerical calculations have been performed to obtain the exact infinite-temperature time-dependent spin autocorrelation function $G(t)$ for a linear chain of $N$ spins ( $S=\frac{1}{2}$ ) interacting by nearest-neighbor Heisenberg exchange for $N=5, 7, 9 \mathrm{and} 11$ by a method different from that of Carboni and Richards. Exact results for the first 20 moments and estimates for ${M}_{22}$ to ${M}_{30}$ of the frequency autocorrelation function for the infinite chain are provided. Excellent agreement is obtained with some recent results obtained by Morita, who, however, gives terms only up to ${M}_{10}$ . $G(t)$ does not show a simple monotonic diffusive ($\ensuremath{\sim}{t}^{\ensuremath{-}\frac{1}{2}}$) behavior within $\frac{4\ensuremath{\hbar}}{J}$, the time domain up to which we believe our result for $N=11$ to be equivalent to that of the infinite chain although it is reduced to about 10% of its value at $t=0$ .Numerical calculations have been performed to obtain the exact infinite-temperature time-dependent spin autocorrelation function $G(t)$ for a linear chain of $N$ spins ($S=\frac{1}{2}$) interacting by nearest-neighbor Heisenberg exchange for $N=5, 7, 9 \mathrm{and} 11$ by a method different from that of Carboni and Richards. Exact results for the first 20 moments and estimates for ${M}_{22}$ to ${M}_{30}$ of the frequency autocorrelation function for the infinite chain are provided. Excellent agreement is obtained with some recent results obtained by Morita, who, however, gives terms only up to ${M}_{10}$. $G(t)$ does not show a simple monotonic diffusive ($\ensuremath{\sim}{t}^{\ensuremath{-}\frac{1}{2}}$) behavior within $\frac{4\ensuremath{\hbar}}{J}$, the time domain up to which we believe our result for $N=11$ to be equivalent to that of the infinite chain although it is reduced to about 10% of its value at $t=0$.

Physical review. B, Solid stateMar 1, 197528 citations

Autocorrelation function of the Heisenberg ferromagnet at elevated temperatures

T. Morita, Katsushi Kobayashi, Seiichiro Katsura +1 more

Physics Letters AAug 1, 19709 citations

The spectral densities of dynamical spin autocorrelation functions at infinite temperature are studied for the S=1/2XXZ model (with exchange couplings

{\mathit{J}}_{\mathit{x}}

{\mathit{J}}_{\mathit{y}}

\ensuremath{\equiv}J,

{\mathit{J}}_{\mathit{z}}

) on the linear chain, the square lattice, and the simple cubic lattice. The low-frequency behavior of a given spectral density is inferred from certain characteristic properties of its continued-fraction coefficients as determined from computed frequency moments. The analysis yields estimates for the

{\mathit{J}}_{\mathit{z}}

/J dependence of the infrared-singularity exponent. In the d=1 case, the exponent for spin fluctuations perpendicular to the O(2) symmetry axis responds sensitively as the anisotropy parameter sweeps across the O(3) symmetry point

{\mathit{J}}_{\mathit{z}}

/J=1, while the exponent for the parallel fluctuations shows little variation. In the cases d=2 and d=3 the same observations are made for autocorrelation functions of aggregate spins in chains and lattice planes, respectively.

Numerical calculations have been performed to obtain the exact infinite-temperature time-dependent spin autocorrelation function

G(t)

for a linear chain of

N

spins (

S=\frac{1}{2}

) interacting by nearest-neighbor Heisenberg exchange for

N=5, 7, 9 \mathrm{and} 11

by a method different from that of Carboni and Richards. Exact results for the first 20 moments and estimates for

{M}_{22}

{M}_{30}

of the frequency autocorrelation function for the infinite chain are provided. Excellent agreement is obtained with some recent results obtained by Morita, who, however, gives terms only up to

{M}_{10}

G(t)

does not show a simple monotonic diffusive ($\ensuremath{\sim}{t}^{\ensuremath{-}\frac{1}{2}}$) behavior within $\frac{4\ensuremath{\hbar}}{J}$, the time domain up to which we believe our result for

N=11

to be equivalent to that of the infinite chain although it is reduced to about 10% of its value at

t=0