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Some measurements are non-local, e.g., the correlation
function 
.
This can also be easily calculated in parallel, by continually shifting
a copy of the spin variables one site at a time.
-
After the first shift, every (abstract) processor calculates the local value
of
, i.e., 
, at each site, and the sum over sites is
taken (e.g. using SUM).
-
After the second shift every processor calculates the local value of
, and the sum over sites is done.
-
This is continued until the spin has been shifted halfway around the lattice
(only halfway due to periodic boundary conditions).
For message passing languages it is more efficient to only do the partial
sums on each processor after every shift.
The global sums are done at the end on the vector 
rather than
each of the individual values 
, ... in turn,
so as to reduce latency.
Paul Coddington, Northeast Parallel Architectures Center at Syracuse University, paulc@npac.syr.edu