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Differential renormalization of van der Waals spin models

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Abstract

An exact renormalization group equation in differential form is derived for spin systems with general many-body interactions in the van der Waals limit. This equation is solved and the free energy is determined as an integral along the renormalization trajectory in the interaction space. It is shown that the transformation can always be modified in such a way that an undetermined integration constant for the free energy vanishes exactly, also below the critical temperature. We also demonstrate how the invariance of the free energy under a parameterdependent equivalence transformation can provide information about the critical behavior of the system. In this alternative approach “dangerous” irrelevant variables play an essential role.

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Author notes

  1. Attilio Stella

    Present address: Istituto di Fisica e Unità GNSM del CNR, Università di Padova, Padova, Italy

Authors and Affiliations

  1. Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Leuven, Belgium

    Raf Dekeyser & Attilio Stella

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  1. Raf Dekeyser
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  2. Attilio Stella
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On leave of absence from Istituto di Fisica e Unità GNSM del CNR, Università di Padova, Padova, Italy.

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Dekeyser, R., Stella, A. Differential renormalization of van der Waals spin models. J Stat Phys 23, 587–607 (1980). https://doi.org/10.1007/BF01011731

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  • DOI: https://doi.org/10.1007/BF01011731

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