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Scaling laws at the phase transition of systems with divergent order parameter and/or internal length: The example of DNA denaturation

Sahin Buyukdagli and Marc Joyeux*

  • Laboratoire de Spectrométrie Physique (CNRS UMR 5588), Université Joseph Fourier, BP 87, 38402 St Martin d’Hères, France

  • *Electronic address: Marc.JOYEUX@ujf-grenoble.fr
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Phys. Rev. E 73, 051910 – Published 19 May, 2006

DOI: https://doi.org/10.1103/PhysRevE.73.051910

Abstract

We used the transfer-integral method to compute, with an uncertainty smaller than 5%, the six fundamental characteristic exponents of two dynamical models for DNA thermal denaturation and investigate the validity of the scaling laws. Doubts concerning this point arise because the investigated systems (i) have a divergent internal length, (ii) are described by a divergent order parameter, and (iii) are of dimension 1. We found that the assumption that the free energy can be described by a single homogeneous function is robust, despite the divergence of the order parameter, so that Rushbrooke’s and Widom’s identities are valid relations. Josephson’s identity is instead not satisfied. This is probably due to the divergence of the internal length, which invalidates the assumption that the correlation length is solely responsible for singular contributions to thermodynamic quantities. Fisher’s identity is even more wrong. We showed that this is due to the d=1 dimensionality and obtained an alternative law, which is well satisfied at DNA thermal denaturation.

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Phys. Rev. E 73, 051910– Published 19 May, 2006
  • Received 24 February 2006

© 2006 American Physical Society

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