Self Avoiding Walks in Four Dimensions: Logarithmic Corrections
  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. 
Peter Grassberger, Rainer Hegger and Lothar Schaefer