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

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

2005-11-03

arxiv.org/abs/cond-mat/0511072v1

J. Stat. Mech. (2005) P12011

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages,6 figures

Scientific paper

10.1088/1742-5468/2005/12/P12011

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 $.

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