A General Theory of the Second Order Phase Transition. I

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概要

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• 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[{η_q}: T] is introduced. It is a functional of the Fourier component η_q of the local order parameter η(r). A general property of the correlation function <η_qη_<-q>> is established rigorously. The equilibrium free energy and the wave-number dependent susceptibility X_g are expressed in terms of the linked clusters, large clusters corresponding to higher 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 X_q'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.

• 社団法人日本物理学会の論文
• 1967-01-05

著者

• IZUYAMA Takeo

  Institute of Physics,College of Arts and Science,University of Tokyo

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