Hierarchical pinning model with site disorder: Disorder is marginally relevant

DOI10.1007/s00440-009-0226-6zbMath1201.60095arXiv0807.4864OpenAlexW2068430854MaRDI QIDQ5961960

Hubert Lacoin

Publication date: 16 September 2010

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.4864

zbMATH Keywords

quenched disordercritical behaviourdiamond latticehierarchical pinning model

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random dynamical systems (37H99)

Related Items (15)

Hierarchical pinning models, quadratic maps and quenched disorder ⋮ The intermediate disorder regime for a directed polymer model on a hierarchical lattice ⋮ Hierarchical pinning model in correlated random environment ⋮ Disorder relevance at marginality and critical point shift ⋮ PINNING ON A DEFECT LINE: CHARACTERIZATION OF MARGINAL DISORDER RELEVANCE AND SHARP ASYMPTOTICS FOR THE CRITICAL POINT SHIFT ⋮ Nested critical points for a directed polymer on a disordered diamond lattice ⋮ A Max-Type Recursive Model: Some Properties and Open Questions ⋮ An exactly solvable continuous-time Derrida-Retaux model ⋮ Directed polymers on hierarchical lattices with site disorder ⋮ The free energy in the Derrida-Retaux recursive model ⋮ The depinning transition in presence of disorder: a toy model ⋮ Continuum directed random polymers on disordered hierarchical diamond lattices ⋮ Results and conjectures on a toy model of depinning ⋮ High-temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder ⋮ Marginal relevance of disorder for pinning models

Cites Work

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• The effect of disorder on polymer depinning transitions
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• Disordered pinning models and copolymers: Beyond annealed bounds
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• Effect of disorder on two-dimensional wetting
• Equality of critical points for polymer depinning transitions with loop exponent one
• Hierarchical pinning models, quadratic maps and quenched disorder
• Marginal relevance of disorder for pinning models
• Fractional moment bounds and disorder relevance for pinning models

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