2001/07/06 by Viktoria Blavatska, Victoria Blavats'ka, Christian von Ferber +1
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.1103/physreve.64.041102
published as Phys. Rev. E 64 (2001) 041102 · 13 pages, 5 figures
arxiv created 2001/07/06 · openalex publication_date 2001/09/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We study the scaling properties of polymers in a d-dimensional medium with quenched defects that have power law correlations approximately r(-a) for large separations r. This type of disorder is known to be relevant for magnetic phase transitions. We find strong evidence that this is true also for the polymer case. Applying the field-theoretical renormalization group approach we perform calculations both in a double expansion in epsilon=4-d and delta=4-a up to the one-loop order and second in a fixed dimension (d=3) approach up to the two-loop approximation for different fixed values of the correlation parameter, 2<or=a<or=3. In the latter case the numerical results need appropriate resummation. We find that the asymptotic behavior of self-avoiding walks in three dimensions and long-range-correlated disorder is governed by a set of separate exponents. In particular, we give estimates for the nu and gamma exponents as well as for the correction-to-scaling exponent omega. The latter exponent is also calculated for the general m-vector model with m=1,2,3.