Copolymer Networks: Multifractal dimension spectra in polymer field theory

Abstract

We explore the rich scaling behavior of copolymer networks in solution. We establish a field theoretic description in terms of composite operators. Our 3rd order resummation of the spectrum of scaling dimensions brings about remarkable features: Convexity of the spectra allows for a multifractal interpretation. This has not been conceived for power of field operators of ${\varphi }^4$ field theory before. The 2D limit of the mutually avoiding walk star apparently corresponds to results of a conformal Kac series. Such a classification seems not possible for the 2D limit of other copolymer stars. The 3rd order calculation of a large collection of exponents furthermore allows for a consistency check of two complementary schemes: epsilon expansion and renormalization at fixed dimension.

7 pages, revtex, 1 latex picture

References in corpus (3)

• Polymers and percolation in two dimensions and twisted N=2 supersymmetry
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Multifractal Dimensions for Branched Growth

Cited by in corpus (16)

• Pseudo--epsilon expansion of six--loop renormalization group functions of an anisotropic cubic model
• Two-Dimensional Copolymers and Exact Conformal Multifractality
• Copolymer Networks and Stars: Scaling Exponents
• Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
• Multifractality of Brownian motion near absorbing polymers
• Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution
• Universality classes of three-dimensional $mn$-vector model
• Entropy-induced separation of star polymers in porous media
• Critical behaviour of the O(n)-${\varphi }^4$ model with an antisymmetric order parameter
• Star copolymers in porous environments: scaling and its manifestations
• Scaling of star polymers: high order results
• Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results
• Multifractal properties of resistor diode percolation
• Variety of Scaling Laws for DNA Thermal Denaturation
• Scaling of complex polymers: new universality classes and beyond
• DNA thermal denaturation by polymer field theory approach: effects of the environment