Delocalization transition of the selective interface model: distribution of pseudo-criticaltemperatures

Abstract

According to recent progress in the finite size scaling theory of critical disordered systems, thenature of the phase transition is reflected in the distribution of pseudo-critical temperaturesTc(i, L) over the ensembleof samples (i) of size L. In this paper, we apply this analysis to the delocalization transition ofa heteropolymeric chain at a selective fluid–fluid interface. The widthΔTc(L) and the shift [Tc(∞) - Tcav(L)] are found to decay with the same exponentL−1/νR,where 1/νR ∼ 0.26. The distribution of pseudo-critical temperaturesTc(i, L) is clearly asymmetric, and is well fitted by a generalized Gumbel distribution of parameterm ∼ 3. We also consider the free energy distribution, which can also be fitted by ageneralized Gumbel distribution with a temperature dependent parameter, of orderm ∼ 0.7 in the critical region. Finally, the disorder averaged number of contacts with the interface scales atTc asLρ with ρ ∼ 0.26 ∼ 1/νR.