  We present a very simple proof that the $O(n)$ model satisfies a uniform
logarithmic Sobolev inequality (LSI) if the positive definite coupling matrix
has largest eigenvalue less than $n$. This condition applies in particular to
the SK spin glass model at inverse temperature $\beta < 1/4$. It is the first
result of rapid relaxation for the SK model and requires significant
cancellations between the ferromagnetic and anti-ferromagnetic spin couplings
that cannot be obtained by existing methods to prove Log-Sobolev inequalities.
The proof also applies to more general bounded and unbounded spin systems. It
uses a single step of zero range renormalisation and Bakry--Emery theory for
the renormalised measure.
