Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
| dc.creator | Monthus, Cecile | |
| dc.creator | Garel, Thomas | |
| dc.date | 2005-09-19 | |
| dc.date.accessioned | 2026-07-07T06:41:48Z | |
| dc.date.available | 2026-07-07T06:41:48Z | |
| dc.description | 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 $T_c(i,L)$ 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 $T_c(i,L)$ with mean $T_c^{av}(L)$ and width $ΔT_c(L)$. For the marginal case $c=1.5$ corresponding to two-dimensional wetting, both the width $ΔT_c(L)$ and the shift $[T_c(\infty)-T_c^{av}(L)]$ decay as $L^{-1/2}$, so the exponent is unchanged ($ν_{random}=2=ν_{pure}$) but disorder is relevant and leads to non self-averaging at criticality. For relevant disorder $c=1.75$, the width $ΔT_c(L)$ and the shift $[T_c(\infty)-T_c^{av}(L)]$ decay with the same new exponent $L^{-1/ν_{random}}$ (where $ν_{random} \sim 2.7 > 2 > ν_{pure}$) 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 $ΔT_c(L) \sim L^{-1/2}$ dominates over the shift $[T_c(\infty)-T_c^{av}(L)] \sim L^{-1}$, i.e. there are two correlation length exponents $ν=2$ and $\tilde ν=1$ that govern respectively the averaged/typical loop distribution. | |
| dc.description | 15 pages; 8 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0509479 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0509479 | |
| dc.identifier | Eur. Phys. J. B 48, 393-403 (2005) | |
| dc.identifier | doi:10.1140/epjb/e2005-00417-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101806 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Probability | |
| dc.title | Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents | |
| dc.type | text |