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Log-periodic Critical Amplitudes: A Perturbative Approach

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Abstract

Log-periodic amplitudes appear in the critical behavior of a large class of systems, in particular when a discrete scale invariance is present. Here we show how to compute these critical amplitudes perturbatively when they originate from a renormalization map which is close to a monomial. In this case, the log-periodic amplitudes of the subdominant corrections to the leading critical behavior can also be calculated.

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Acknowledgements

The authors acknowledge the support of ANR, grant SHEPI.

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Authors and Affiliations

  1. Laboratoire de Physique Statistique, École Normale Supérieure, Université Pierre et Marie Curie, Université Paris Diderot, CNRS, 24, rue Lhomond, 75231, Paris Cedex 05, France

    Bernard Derrida

  2. U.F.R. Mathématiques, Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot, Bât. Sophie Germain, 5 rue Thomas Mann, 75205, Paris Cedex 13, France

    Giambattista Giacomin

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  1. Bernard Derrida
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  2. Giambattista Giacomin
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Correspondence to Giambattista Giacomin.

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Dedicated to Herbert Spohn, our colleague, friend and source of inspiration, on the occasion of his 65th birthday.

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Derrida, B., Giacomin, G. Log-periodic Critical Amplitudes: A Perturbative Approach. J Stat Phys 154, 286–304 (2014). https://doi.org/10.1007/s10955-013-0774-0

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