A phase transition is marked by abrupt macroscopic changes as external parameters are changed, such as an increase of temperature. The point where a phase transition takes place is called a critical point.
We distinguish normally between two types of phase transitions; first-order transitions and second-order transitions. An important quantity in studies of phase transitions is the so-called correlation length \( \xi \) and various correlations functions like spin-spin correlations. For the Ising model we shall show below that the correlation length is related to the spin-correlation function, which again defines the magnetic susceptibility. The spin-correlation function is nothing but the covariance and expresses the degree of correlation between spins.