# 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:

[itex]G(x,x') = \langle s(x)s(x') \rangle.[itex]

This function is equal to unity when [itex]x=x'[itex] and decreases as the distance [itex]|x-x'|[itex] 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 [itex]|x-x'|[itex] 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.

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