Long-range_order

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:

$G(x,x\backslash \text{'})\; =\; \backslash langle\; s(x)s(x\backslash \text{'})\; \backslash rangle.$

This function is equal to unity when $x=x\backslash \text{'}$ and decreases as the distance $|x-x\backslash \text{'}|$ 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 $|x-x\backslash \text{'}|$ 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

• order-disorder

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