dorsal/arxiv
View SchemaOn scaling laws at the phase transition of systems with divergent order parameter and/or internal length : the example of DNA denaturation
| Authors | Sahin Buyukdagli, Marc Joyeux |
|---|---|
| Categories | |
| ArXiv ID | physics/0604076 |
| URL | https://arxiv.org/abs/physics/0604076 |
| DOI | 10.1103/PhysRevE.73.051910 |
| Journal | Physical Review E 73 (2006) 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, (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.
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"abstract": "We used the Transfer-Integral method to compute, with an uncertainty smaller\nthan 5%, the six fundamental characteristic exponents of two dynamical models\nfor DNA thermal denaturation and investigate the validity of the scaling laws.\nDoubts concerning this point arise because the investigated systems (i) have a\ndivergent internal length, (ii) are described by a divergent order parameter,\n(iii) are of dimension 1. We found that the assumption that the free energy can\nbe described by a single homogeneous function is robust, despite the divergence\nof the order parameter, so that Rushbrooke\u0027s and Widom\u0027s identities are valid\nrelations. Josephson\u0027s identity is instead not satisfied. This is probably due\nto the divergence of the internal length, which invalidates the assumption that\nthe correlation length is solely responsible for singular contributions to\nthermodynamic quantities. Fisher\u0027s identity is even wronger. We showed that\nthis is due to the d=1 dimensionality and obtained an alternative law, which is\nwell satisfied at DNA thermal denaturation.",
"arxiv_id": "physics/0604076",
"authors": [
"Sahin Buyukdagli",
"Marc Joyeux"
],
"categories": [
"physics.bio-ph",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevE.73.051910",
"journal_ref": "Physical Review E 73 (2006) 051910",
"title": "On scaling laws at the phase transition of systems with divergent order parameter and/or internal length : the example of DNA denaturation",
"url": "https://arxiv.org/abs/physics/0604076"
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