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

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, (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 wronger. We showed that this is due to the d=1 dimensionality and obtained an alternative law, which is well satisfied at DNA thermal denaturation.

accepted in Phys. Rev. E

References in corpus (2)

• Dynamical model based on finite stacking enthalpies for homogeneous and inhomogeneous DNA thermal denaturation
• Towards more realistic dynamical models for DNA secondary structure

Cited by in corpus (12)

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• Dynamical versus statistical mesoscopic models for DNA denaturation
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• Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide
• Theoretical investigation of finite size effects at DNA melting
• Numerical evidence for relevance of disorder in a Poland-Scheraga DNA denaturation model with self-avoidance: Scaling behavior of average quantities
• Renormalisation group determination of the order of the DNA denaturation transition
• Mapping between the order of thermal denaturation and the shape of the critical line of mechanical unzipping in 1-dimensional DNA models
• Geometry for a `penguin-albatross' rookery
• On the Pseudo-Schrödinger Equation approximation of the Transfer-Integral operator for 1-dimensional DNA models