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In publications on dilute spin glass moment dynamics probed by *µSR*,
Uemura[1] modeled the Lorentzian field distribution at the muon site
due to the dilute spins

as a Gaussian distribution of fields at each "class'' of muon site

convoluted with a strange distribution of such classes of site (see Fig.1)

This convolution also works to generate the distribution of magnitudes of
field:

where

and to generate the static ZF Lorentzian Kubo-Toyabe relaxation function:

where

Figure 1: Uemura's trick distribution

In spite of the apparent strangeness
,
Uemura was able to
use this to model moment dynamics (for a stationary muon) to produce dynamic
muon spin relaxation functions *G*(*t*) that decoupled properly in the fast
fluctuation limit (direct "dynamicization'' of the Lorentzian field
distribution, equivalent muon diffusion in a the spin glass, does not result
in fluctuation decoupling), and were consistent with observed *µSR*. So,
this convolution does seem to bear some relation to reality.

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*Jess H. Brewer *

2002-09-24