Long-range correlation
The expression 'long-range correlation' specifically refers to the slow decay of the (temporal or spatial) correlation function.
Ignoring coherent states ('modes', to which the concept does not apply), the correlation function typically decays exponentially and can be characterized by a 'decorrelation time' (or length), calculated as the distance at which the correlation has dropped from its maximum value by an amount 1/e.
When the correlation exhibits a slower decay for large values of the delay (or distance) Δ, namely an algebraic decay proportional to 1/Δα (α > 0 but not too large, < 2), the correlations at large delay may be quite important to understand the global system behaviour (contrasting sharply with the exponential decay case, in which large values of Δ can be safely ignored).[1]
This unusual, slow decay of the correlation function has important consequences, implying that the system exhibits 'memory effects' or 'non-local behaviour', which can be understood in the framework of Self-Organised Criticality and the concept of self-similarity. Also see Non-diffusive transport and Continuous Time Random Walk.