The correlation function in statistical mechanics is measure of the order in a system. It tells us how microscopic variables at different positions are correlated. In a spin system, it is the thermal average of the scalar product of the spins at two lattice points over all possible orderings. The correlation function is hence, For stochastic processes, including those that arise in statistical mechanics and Euclidean quantum field theory, a correlation function is the correlation between random variables at two different points in space or time. ... Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... The terms spin and SPIN have several meanings, including those primarily discussed as spinning: For spin in sub-atomic physics, see spin (physics) For the stalled aircraft maneuver or any of several forms of loss of control in aircraft, see spin (flight) For the periodical, see Spin Magazine For the...

Even in a disordered phase,spins at different positions are correlated. The alignment that would naturally result as a result of the interaction between spins is destroyed by thermal effects. At high temperatures one sees an exponential correlation with the correlation function being given by,

where ξ is what is called the correlation length, r is the distance between spins and d is the dimension of the system. As the temperature is lowered, thermal disordering is lowered and the correlation length increases. In second order phase transitions, the correlation length diverges at the critical point, leading to a power law correlation, that is responsible for scaling, seen in these transitions. The power in the power law is independent of temperature. In physics, a phase transition is the transformation of a thermodynamic system from one phase to another. ... Chemistry In chemistry, a critical point is the conditions ( temperature, pressure) at which the liquid state of the matter ceases to exist. ... See Also: Watt In physics, a power law relationship between two scalar quantities x and y is any such that the relationship can be written as where a (the constant of proportionality) and k (the exponent of the power law) are constants. ... The term scaling can have several manings: Scaling can be defined as the determination of the interdependency of variables in a physical system. ...

It is in fact universal, i.e found to be the same in a wide variety of systems. Universal has several meanings: For the concept of a universal in metaphysics, see Universal (metaphysics). ...