Polymers in long-range-correlated disorder

Abstract

We study the scaling properties of polymers in a d-dimensional medium with quenched defects that have power law correlations ~r^{-a} for large separations r. This type of disorder is known to be relevant for magnetic phase transitions. We find strong evidence that this is true also for the polymer case. Applying the field-theoretical renormalization group approach we perform calculations both in a double expansion in epsilon=4-d and delta=4-a up to the 1-loop order and secondly in a fixed dimension (d=3) approach up to the 2-loop approximation for different fixed values of the correlation parameter, 2=<a=<3. In the latter case the numerical results need appropriate resummation. We find that the asymptotic behavior of self-avoiding walks in three dimensions and long-range-correlated disorder is governed by a set of separate exponents. In particular, we give estimates for the 'nu' and 'gamma' exponents as well as for the correction-to-scaling exponent 'omega'. The latter exponent is also calculated for the general m-vector model with m=1,2,3.

13 pages, 5 figures

References in corpus (1)

• `Generalized des Cloizeaux' exponent for self-avoiding walks on the incipient percolation cluster

Cited by in corpus (32)

• Public transport networks: empirical analysis and modeling
• Critical behavior of the 2D Ising model with long-range correlated disorder
• Critical behavior of magnetic systems with extended impurities in general dimensions
• Critical dynamics and effective exponents of magnets with extended impurities
• Shapes of macromolecules in good solvents: field theoretical renormalization group approach
• Monte-Carlo study of anisotropic scaling generated by disorder
• Entropy-induced separation of star polymers in porous media
• Universal features of polymer shapes in crowded environment
• Disorder effects on the static scattering function of star branched polymers
• Ring polymers in crowded environment: conformational properties
• Star copolymers in porous environments: scaling and its manifestations
• Two-dimensional Ising model with self-dual biaxially correlated disorder
• Equivalence of quenched and annealed averaging in models of disordered polymers
• Spreading processes in "post-epidemic" environments
• The influence of long-range correlated defects on critical ultrasound propagation in solids
• Scaling laws for random walks in long-range correlated disordered media
• Influence of long-range correlated quenched disorder on the adsorption of long flexible polymer chains on a wall
• Three-dimensional Ising model confined in low-porosity aerogels: a Monte Carlo study
• Vicious walks with long-range interactions
• Polymers in disordered environments
• Conformational properties of polymers in anisotropic environments
• Dynamics of linear polymers in random media
• Two-loop Feynman integrals for ${\varphi }^4$ theory with long-range correlated disorder
• Universal size properties of "star-ring" polymer structure in disordered environment
• Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains
• Loop formation in polymers in crowded environment
• Probability of loops formation in star polymers in long range correlated disorder
• Emergent universal critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of correlated disorder
• Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement Measures
• Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects
• Randomly charged polymers in porous environment
• DNA thermal denaturation by polymer field theory approach: effects of the environment