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:

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

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

Statistical mechanics | 長距離秩序