Nonlongrange

Nonlongrange is a term used across disciplines to describe systems, models, or phenomena in which interactions or correlations do not extend indefinitely but decay rapidly with distance or time. It is not a formal technical term with a universal definition, but a descriptive label used to distinguish nonlong-range behavior from long-range phenomena characterized by slow, power-law, or non-summable decay.

In physics, nonlongrange typically refers to systems with finite interaction range or short-range correlations. The correlation function C(r) decays exponentially or faster, yielding a finite correlation length. This property is common in many lattice spin models with nearest-neighbor couplings and in many fluids away from critical points. The absence of long-range order and the lack of critical fluctuations are typical of nonlongrange regimes, though exceptions exist near certain phase boundaries.

In time-series analysis and probability, nonlongrange describes processes with short memory, where autocorrelation decays rapidly (often exponentially), and the variance of partial sums grows linearly with sample size. This contrasts with long-range dependent processes that show slowly decaying autocovariances and nonstandard scaling. Common examples of nonlongrange models include ARMA processes. Implications include standard central limit behavior and conventional statistical inference.

In network theory and computation, nonlongrange may refer to networks with predominantly local or finite-range connections, as opposed to networks with long-range links that enable small-world effects. The term is less formal in this context and is often used descriptively.