2003/06/12 by Nikos Theodorakopoulos · 3 citations
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.026109
published as Phys. Rev E 68, 026109 (2003) · 5 pages, 6 figures, subm. to Phys. Rev. E
arxiv created 2003/06/12 · openalex publication_date 2003/08/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
One-dimensional thermodynamic instabilities are phase transitions, not prohibited by Landau's argument because the energy of the domain wall which separates the two phases is infinite. Whether they actually occur in a given system of particles must be demonstrated on a case-by-case basis by examining the properties of the corresponding singular transfer integral (TI) equation. The present work deals with the generic Peyrard-Bishop model of DNA denaturation. In the absence of exact statements about the spectrum of the singular TI equation, I use Gauss-Hermite quadratures to achieve a single-parameter-controlled approach to rounding effects; this allows me to employ finite-size scaling concepts in order to demonstrate that a phase transition occurs and to derive the critical exponents.