Eur. Phys. J. B 48, 393-403 (2005)
https://doi.org/10.1140/epjb/e2005-00417-7

Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents

Service de Physique Théorique, CEA/DSM/SPhT, Unité de recherche associée au CNRS, 91191 Gif-sur-Yvette Cedex, France

Corresponding author: ^a garel@spht.saclay.cea.fr

Received: 20 September 2005
Published online: 23 December 2005

Abstract

According to recent progresses in the finite size scaling theory of disordered systems, thermodynamic observables are not self-averaging at critical points when the disorder is relevant in the Harris criterion sense. This lack of self-averageness at criticality is directly related to the distribution of pseudo-critical temperatures over the ensemble of samples (i) of size L. In this paper, we apply this analysis to disordered Poland-Scheraga models with different loop exponents c, corresponding to marginal and relevant disorder. In all cases, we numerically obtain a Gaussian histogram of pseudo-critical temperatures with mean and width . For the marginal case c=1.5 corresponding to two-dimensional wetting, both the width and the shift decay as , so the exponent is unchanged () but disorder is relevant and leads to non self-averaging at criticality. For relevant disorder c=1.75, the width and the shift decay with the same new exponent (where ) and there is again no self-averaging at criticality. Finally for the value c=2.15, of interest in the context of DNA denaturation, the transition is first-order in the pure case. In the presence of disorder, the width dominates over the shift , i.e. there are two correlation length exponents and that govern respectively the averaged/typical loop distribution.