A correlation length is a spatial scale extracted from the decay of a correlation function. For a nonnegative
lattice correlation 
along a coordinate axis, the exponential correlation length
is 
,
where
 |
provided the limit exists and is positive. A different convention is the second-moment correlation length. For a summable translation-invariant
correlation 
on 
, with positive susceptibility
and finite second moment, it is
 |
These two definitions need not give the same value.
