Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures

TL;DR

This study investigates the distribution of pseudo-critical temperatures in the delocalization transition of heteropolymeric chains at interfaces, revealing asymmetric distributions and scaling behaviors consistent with finite size scaling theory.

Contribution

It applies finite size scaling analysis to the delocalization transition, characterizing the distribution of pseudo-critical temperatures and free energy, and identifying their scaling exponents and distribution shapes.

Findings

Distribution of pseudo-critical temperatures is asymmetric and fits a generalized Gumbel distribution.

Width and shift of the pseudo-critical temperature distribution decay with the same exponent.

Number of contacts with the interface scales with system size as L^{0.26}.

Abstract

According to recent progress in the finite size scaling theory of critical disordered systems, the nature of the phase transition is reflected in 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 the delocalization transition of an heteropolymeric chain at a selective fluid-fluid interface. The width $\Delta T_c(L)$ and the shift $[T_c(\infty)-T_c^{av}(L)]$ are found to decay with the same exponent $L^{-1/\nu_{R}}$, where $1/\nu_{R} \sim 0.26$. The distribution of pseudo-critical temperatures $T_c(i,L)$ is clearly asymmetric, and is well fitted by a generalized Gumbel distribution of parameter $m \sim 3$. We also consider the free energy distribution, which can also be fitted by a generalized Gumbel distribution with a temperature dependent parameter, of order $m \sim 0.7$ in the critical region. Finally, the disorder averaged number of contacts with the interface scales at $T_c$ like $L^{\rho}$ with $\rho \sim 0.26 \sim 1/\nu_R $.