Theta-point exponent for polymer chain in random media

Abstract

Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentrationp, we show that theθ-point size exponentϑ of polymer chains remains unchanged for small disorder concentration (p>p c ). At the percolation thresholdp=p c , using a Flory-type approximation, we conjecture thatϑ =5/(d B +7), whered B is the percolation backbone dimension. It shows that the upper critical dimensionality for theθ-point transition atp=p c shifts to a dimensiond c >3. We also propose that theθ-point varies practically linearly withp for 1>p⩾p c .