Self Avoiding Walks in Four Dimensions: Logarithmic Corrections

TL;DR

This paper reports simulation results for long self-avoiding walks in four dimensions, highlighting the presence of logarithmic corrections and comparing these findings with theoretical predictions from renormalization group and field theory.

Contribution

It provides new simulation data for self-avoiding walks in four dimensions and compares these with advanced theoretical models, revealing complexities in asymptotic behavior.

Findings

Indications of logarithmic corrections in four-dimensional self-avoiding walks

Poor fit of data to leading asymptotic terms

Comparison with renormalization group and field theory results

Abstract

We present simulation results for long ($N\leq 4000$) 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.