3 years ago

Self-Avoiding Walk on the square site-diluted Ising-correlated lattice.

A. Saber, H. Mohammadzadeh, M. N. Najafi, J. Cheraghalizadeh

The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean field relation is tested to measure the effect of correlation. After exploring a perturbative Fokker-Planck-like equation, we apply an enriched Rosenbluth Monte Carlo method to study the problem. To be more precise, the winding angel analysis is also performed from which the diffusivity parameter of Schramm-Loewner evolution (SLE) theory ($\kappa$) is extracted. We find that at the critical Ising (host) system the exponents are in agreement with the Flory's approximation. For the off-critical Ising system we find also a new behavior for the fractal dimension of the walker trace in terms of the correlation length of the Ising system $\xi(T)$, i.e. $D_F^{\text{SAW}}(T)-D_F^{\text{SAW}}(T_c)\sim \frac{1}{\sqrt{\xi(T)}}$.

Publisher URL: http://arxiv.org/abs/1801.08962

DOI: arXiv:1801.08962v1

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.