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

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 $\rho \sim 0.26\sim 1/{\nu }_R$.

9 pages,6 figures

References in corpus (4)

• Global fluctuations and Gumbel statistics
• Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media
• Estimates on path delocalization for copolymers at selective interfaces
• Two-dimensional wetting with binary disorder: a numerical study of the loop statistics

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