Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach

Details Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach

2003-06-12

arxiv.org/abs/cond-mat/0306315v1

Phys. Rev E 68, 026109 (2003)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 6 figures, subm. to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.68.026109

One-dimensional thermodynamic instabilities are phase transitions not prohibited by Landau's argument, because the energy of the domain wall (DW) 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 (non-) analyticity properties of the corresponding transfer integral (TI) equation. The present note 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.

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