Dynamic structure factor for a ferromagnet in the scaling region to first order in $ε = 6 - d$

The dynamic structure factor for a model ferromagnet is calculated to order

ε = 6 - d

for

T \geq T_{c}

. The dynamic shape function is extracted from the structure factor and plotted for various values of

ε

and

x = k ξ

, where

ξ

is the correlation length and

k

the wave number. In the vicinity of

T_{c}

and for

ε ≳ 0.95

peaks appear which are characteristic of sloppy spin-wave modes.

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Dynamic structure factor for a ferromagnet in the scaling region to first order inε=6−d