In this chapter we discuss the nature of phase transitions with reference to experimental results and introduce the idea of universality. The geometry of the possible types of phase transitions is explored, particularly in the case of a two-dimensional phase space. The way that phase transitions are manifested in classical models, in particular the van der Waals fluid, is examined. We consider a coexistence curve terminating at a critical point, where the critical exponents are defined and related by inequalities. The classical results for this case provided by Landau theory are obtained. One of the most powerful elements of the study of critical phenomena developed in the 1960s was phenomenological scaling theory. Whilst scaling theory is closely allied to the use of the renormalization group in statistical mechanics, it stands alone based on the Kadanoff scaling hypothesis as part of thermodynamics. We apply this theory to a critical curve and a critical point and coexistence curve, deriving the scaling laws. Finally we discuss the relationship between scaling theory and universality.

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Phase Transitions and Critical Phenomena

  • David A. Lavis,
  • Roman Frigg

摘要

In this chapter we discuss the nature of phase transitions with reference to experimental results and introduce the idea of universality. The geometry of the possible types of phase transitions is explored, particularly in the case of a two-dimensional phase space. The way that phase transitions are manifested in classical models, in particular the van der Waals fluid, is examined. We consider a coexistence curve terminating at a critical point, where the critical exponents are defined and related by inequalities. The classical results for this case provided by Landau theory are obtained. One of the most powerful elements of the study of critical phenomena developed in the 1960s was phenomenological scaling theory. Whilst scaling theory is closely allied to the use of the renormalization group in statistical mechanics, it stands alone based on the Kadanoff scaling hypothesis as part of thermodynamics. We apply this theory to a critical curve and a critical point and coexistence curve, deriving the scaling laws. Finally we discuss the relationship between scaling theory and universality.