Theta-point exponent for polymer chain in random media

Abstract

Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentration p, we show that the θ-point size exponent ϑ^θ_p of polymer chains remains unchanged for small disorder concentration (p>p_c). At the percolation threshold p=p_c, using a Flory-type approximation, we conjecture that ϑ_pc^θ =5/(d_B+7), where d_B is the percolation backbone dimension. It shows that the upper critical dimensionality for the θ-point transition at p=p_c shifts to a dimension d_c >3. We also propose that the θ-point varies practically linearly with p for 1> p≥ p_c.