Scaling Theories and the Renormalization Group

  • Silvio R. A. Salinas
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


It is too strong to assume that the free energy of a model system in the critical region can be expanded as a power series of the order parameter. The divergent specific heat of the Onsager exact solution for the two-dimensional Ising model precludes an expansion whose coefficients are analytic functions of temperature. In the 1960s, there appeared a number of (weaker) scaling hypotheses, based on some general assumptions about the form of the thermodynamic potentials. Although these scaling hypotheses do not lead to a microscopic treatment of critical phenomena, they do provide a way of going beyond the phenomenological equations of van der Waals and Curie—Weiss. The microscopic justification of these ideas, as well as a real possibility of calculating values for the critical exponents to compare with experimental data and theoretical predictions, were provided by the advent of the modern renormalization-group techniques.


Renormalization Group Ising Model Critical Exponent Recursion Relation Flow Line 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Silvio R. A. Salinas
    • 1
  1. 1.Instituto de FisicaUniversidade de São PaoloSão PaoloBrazil

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