Physical review. B, Condensed matter

Energy fluctuations in a classical Heisenberg chain

Bart De Raedt, Hans A. De Raedt

Published May 1, 1980• 7 citations

Abstract

The time dependence of the energy fluctuations in a classical Heisenberg chain is studied. The exact low-temperature limit is determined, and the time dependence is given by ${J}_{0}(4sin(\frac{1}{2}q)t)$. At nonzero temperatures approximate results are obtained by means of the continued-fraction method. Analytic expressions for the second and fourth frequency moments are given.

DOI: 10.1103/physrevb.21.4108

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Physical review. B, Condensed matter

Energy fluctuations in a classical Heisenberg chain

Bart De Raedt, Hans A. De Raedt

Published May 1, 1980• 7 citations

Publisher

Abstract

The time dependence of the energy fluctuations in a classical Heisenberg chain is studied. The exact low-temperature limit is determined, and the time dependence is given by

{J}_{0}(4sin(\frac{1}{2}q)t)

. At nonzero temperatures approximate results are obtained by means of the continued-fraction method. Analytic expressions for the second and fourth frequency moments are given.

DOI: 10.1103/physrevb.21.4108

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The time dependence of the energy fluctuations in a classical Heisenberg chain is studied. The exact low-temperature limit is determined, and the time dependence is given by

{J}_{0}(4sin(\frac{1}{2}q)t)

. At nonzero temperatures approximate results are obtained by means of the continued-fraction method. Analytic expressions for the second and fourth frequency moments are given.

T=0

result, simple approximations are used to calculate the spectrum. We show rigorously that the time-dependent correlation function is different for ferro-and antiferromagnetic coupling if $T\ensuremath{\ne}0$.

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}

{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

{T}^{2/3}

with a coefficient that depends on the relative fractions of positive and negative bonds. The coefficient is calculated exactly for the equal-probability distribution. There is also a brief analysis of the destabilizing effects of an applied magnetic field.