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.

See also order-disorder

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See also: Long-range order, Correlation, Correlation function, Exponential decay, Order-disorder, Physics, Polynomial, Spin (physics), System