Long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior.
This can be expressed as a correlation function, namely the spin-spin correlation function:
where s is the spin quantum number and x is the distance function within the particular system.
This function is equal to unity when  and decreases as the distance  increases.  Typically, it decays exponentially to zero at large distances, and the system is considered to be disordered. But if the correlation function decays to a constant value at large  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 (for details see Chapter 11 in the textbook cited below. See also Berezinskii–Kosterlitz–Thouless transition). Note that what constitutes a large value of  is understood in the sense of asymptotics.