- Published 2003 in Physical review. E, Statistical, nonlinear, and…

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.

@article{Theodorakopoulos2003ThermodynamicII,
title={Thermodynamic instabilities in one-dimensional particle lattices: a finite-size scaling approach.},
author={Nikos Theodorakopoulos},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2003},
volume={68 2 Pt 2},
pages={026109}
}