抄録
The critical phenomenon of the second order phase transition is considered for temperatures above the critical point. A general phenomenological approach is developed. The generalized free energy F[{ηq}: T] is introduced. It is a functional of the Fourier component ηq of the local order parameter η(r). A general property of the correlation function ⟨ηqη−q⟩ is established rigorously. The equilibrium free energy and the wave-number dependent susceptibility χq are expressed in terms of the linked clusters, large clusters corresponding to highr order fluctuation of the order parameter. The general rule for calculating the contribution of each cluster is given. The rule is shown to be very simple. It is found that the specific heat is expressed as a sum of the temperature derivatives of χq’s. As an example of the application of the linked cluster method, the susceptibility is calculated in the vicinity of the critical point by summing up the clusters that are most divergent when approaching the criticat point. The linked cluster expansion developed here could be a clue to the whole mystery of the singularity at the critical point.
