Long-range order

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

Let us discuss this by 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 posses long-range order. If it decays to zero algebraically (i.e. as a polynomial) then we call it quasi-long-range order.