A renormalization group equation for the inverse propagator is obtained for a stochastic model of isotropic Heisenberg ferromagnet, whose solution at a fixed point yields the dynamical scaling law with the correct dynamic critical exponent. For 6-ε dimensions (ε>0) we describe an iterative method to obtain an ε-expansion for the inverse propagator.

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Erwin Frey, Franz Schwabl

The European Physical Journal BMar 1, 198915 citations

Physics Letters A

On dynamic scaling in the Heisenberg ferromagnet

Sergei V. Maleev

Published Dec 1, 1971• 0 citations

Publisher

DOI: 10.1016/0375-9601(71)90606-2

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The dynamical correlation function

{\mathit{G}}_{\mathbf{r}}

(t)==〈

{\mathbf{S}}_{\mathbf{r}}

(t)\ensuremath{\cdot}

{\mathbf{S}}_{0}

(0)〉 and dynamical structure factor

{\mathit{S}}_{\mathbf{q}}

(\ensuremath{\omega}) are calculated by the modified spin-wave theory for the low-dimensional quantum Heisenberg ferromagnets at low temperature. We use the Dyson-Maleev transformation, ideal spin-wave states, and the rotational averaging.

{\mathit{S}}_{\mathbf{q}}

(\ensuremath{\omega}) satisfies the dynamic scaling relation. The explicit form of the scaling function is obtained. The classical limit of our results is compared with a molecular-dynamics calculation. The agreement is surprisingly good.