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.
Let us discuss this by a correlation function, namely the spin-spin correlation function:
- <math>G(x,x') = \langle s(x)s(x') \rangle.<math>
This function is equal to unity when <math>x=x'<math> and decreases as the distance <math>|x-x'|<math> 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 <math>|x-x'|<math> 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