Long-range order

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In physics, long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior.

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. Typically, it decays exponentially to zero at large distances, and the system is considered to be disordered. 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.