Long-range order - Citizendia

In physics, long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. System (from Latin systēma, in turn from Greek systēma is a set of interacting or interdependent Entities, real or abstract In Probability theory and Statistics, correlation, (often measured as a correlation coefficient) indicates the strength and direction of a linear

This can be seen with a correlation function, namely the spin-spin correlation function:

$G(x,x') = \langle s(x)s(x') \rangle.$

This function is equal to unity when $x = x'$ and decreases as the distance $| x - x' |$ increases. Correlation functions contain information about the distribution of points or events or things across some space/time In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin Typically, it decays exponentially to zero at large distances, and the system is considered to be disordered. A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value If, however, the correlation function decays to a constant value at large $| x - x' |$ then the system is said to possess long-range order. If it decays to zero as a power of the distance then it is called quasi-long-range order.

See also