Scaling behavior of linear polymers in disordered media

Abstract

Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks (SAWs) on percolation clusters and their critical exponent ${\nu }_{\text{SAW}}$, with SAW implicitly referring to \emph{average} SAW. Hitherto, static averaging has been commonly used, e.g. in numerical simulations, to determine what the \emph{average} SAW is. We assert that only kinetic, rather than static, averaging can lead to asymptotic scaling behavior and corroborate our assertion by heuristic arguments and a renormalizable field theory. Moreover, we calculate to two-loop order ${\nu }_{\text{SAW}}$, the exponent ${\nu }_{\text{max}}$ for the longest SAW, and a new family of multifractal exponents ${\nu }^{(\alpha )}$.

4 pages, 3 figures

References in corpus (2)

• The Field Theory Approach to Percolation Processes
• Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster

Cited by in corpus (22)

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• Multifractality of self-avoiding walks on percolation clusters
• Scaling behavior of self-avoiding walks on percolation clusters
• Walking on fractals: diffusion and self-avoiding walks on percolation clusters
• Shapes of macromolecules in good solvents: field theoretical renormalization group approach
• Ring polymers in crowded environment: conformational properties
• Polymers in crowded environment under stretching force: globule-coil transitions
• Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters
• Asymptotic scaling behavior of self-avoiding walks on critical percolation clusters
• Linear Polymers in Disordered Media - the shortest, the longest and the mean(est) SAW on percolation clusters
• Scaling laws for random walks in long-range correlated disordered media
• Polymers in disordered environments
• Polymer collapse of a self-avoiding trail model on a two-dimensional inhomogeneous lattice
• Conformational properties of polymers in anisotropic environments
• Multifractal scaling of flux penetration in the Iron-based Superconductor Ba(Fe${}_{0.93}$Co${}_{0.07}$)${}_2$As${}_2$
• Universal size properties of "star-ring" polymer structure in disordered environment
• Loop formation in polymers in crowded environment
• Lattice models of directed and semiflexible polymers in anisotropic environment
• Density fluctuations of polymers in disordered media
• Probability of loops formation in star polymers in long range correlated disorder
• Distribution functions in percolation problems
• Effect of lattice inhomogeneity on collapsed phases of semi-stiff ISAW polymers