Self Avoiding Walks in Four Dimensions: Logarithmic Corrections

Abstract

We present simulation results for long ($N\le 4000$) self-avoiding walks in four dimensions. We find definite indications of logarithmic corrections, but the data are poorly described by the asymptotically leading terms. Detailed comparisons are presented with renormalization group flow equations derived in direct renormalization and with results of a field theoretic calculation.

NLATEX, 20 pages

Cited by in corpus (24)

• Critical Percolation in High Dimensions
• Theta-point behavior of diluted polymer solutions: Can one observe the universal logarithmic corrections predicted by field theory?
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Scaling of Self-Avoiding Walks in High Dimensions
• Four-dimensional polymer collapse II: Pseudo-First-Order Transition in Interacting Self-avoiding Walks
• Universal scaling behavior of directed percolation around the upper critical dimension
• Logarithmic Corrections in Directed Percolation
• Field theory conjecture for loop-erased random walks
• Renormalization Group Functions of the ϕ^4 Theory in the Strong Coupling Limit: Analytical Results
• Logarithmic corrections to scaling in critical percolation and random resistor networks
• Exact and Monte Carlo study of adsorption of a self-interacting polymer chain for a family of three-dimensional fractals
• Finite-size scaling of directed percolation in the steady state
• Logarithmic Corrections in Dynamic Isotropic Percolation
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Random walk on the range of random walk
• Logarithmic corrections in (4+1)-dimensional directed percolation
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Monte Carlo Simulations of Off-Lattice Polymers
• Four-dimensional polymer collapse II: Interacting self-avoiding trails
• Monte Carlo study of four-dimensional self-avoiding walks of up to one billion steps
• Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions
• Renormalization Group Functions of ϕ^4 Theory from High-Temperature Expansions
• Bethe approximation for the hydrogen-bonding self-avoiding walk in a solvent
• Transport properties of directed percolation clusters at the upper critical dimension