A pr 1 99 5 Optimal self - avoiding paths in dilute random medium

نویسندگان

  • F. Seno
  • A. L. Stella
  • C. Vanderzande
چکیده

By a new type of finite size scaling analysis on the square lattice, and by renormalization group calculations on hierarchical lattices we investigate the effects of dilution on optimal undirected self-avoiding paths in a random environment. The behaviour of the optimal paths remains the same as for directed paths in undiluted medium, as long as forbidden bonds are not exceeding the percolation threshold. Thus, overhanging configurations do not alter the standard self-affine directed polymer scaling regime, even above the directed threshold, when they become unavoidable. When dilution reaches the undirected threshold, the optimal path becomes fractal, with fractal dimension equal to D min , the dimension of the minimal length path on percolation cluster backbone. In this regime the optimal path energy fluctuation, ∆E, can be ascribed entirely to minimal length fluctuations, and satisfies ∆E ∝ L ω , with ω = 1.02 ± 0.06 in 2d, L being the Euclidean distance. Hierarchical lattice calculations confirm that ω is also the exponent of the leading scaling cor-the optimal path does not stick entirely on the minimal length one, obeys R ∼ (∆p) ρ , with ρ ∼ 1.0 ± 0.05 on hierarchical lattices. Such behaviour could be characteristic of the crossover to fractal regime. Transfer matrix results on square lattice show that a similar full sticking does not occur for directed 1 paths at the directed percolation threshold.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

4 A pr 1 99 9 The Upper Critical Dimension of the Abelian Sandpile Model

The existing estimation of the upper critical dimension of the Abelian Sandpile Model is based on a qualitative consideration of avalanches as self-avoiding branching processes. We find an exact representation of an avalanche as a sequence of spanning sub-trees of two-component spanning trees. Using equivalence between chemical paths on the spanning tree and loop-erased random walks, we reduce ...

متن کامل

A pr 2 00 3 Random path representation and sharp correlations asymptotics at high - temperatures

We recently introduced a robust approach to the derivation of sharp asymptotic formula for correlation functions of statistical mechanics models in the high-temperature regime. We describe its application to the nonperturbative proof of Ornstein-Zernike asymptotics of 2-point functions for self-avoiding walks, Bernoulli percolation and ferromagnetic Ising models. We then extend the proof, in th...

متن کامل

A Class of Weakly Self-avoiding Walks

We define a class of weakly self-avoiding walks on the integers by conditioning a simple random walk of length n to have a p-fold self-intersection local time smaller than nβ, where 1 < β < (p+1)/2. We show that the conditioned paths grow of order nα, where α = (p− β)/(p− 1), and also prove a coarse large deviation principle for the order of growth.

متن کامل

Solid Sirolimus Self-microemulsifying Drug Delivery System: Development and Evaluation of Tablets with Sustained Release Property

The clinical application of sirolimus (SRL) as an immunosuppressive agent is largely hampered by its narrow therapeutic range. This study focused on developing SRL tablets with a sustained release profile for better safety. SRL was highly water insoluble and its solubility has been efficiently enhanced by preparing self-microemulsifying drug delivery system (SMEDDS). The SRL-SMEDDS was physical...

متن کامل

Solid Sirolimus Self-microemulsifying Drug Delivery System: Development and Evaluation of Tablets with Sustained Release Property

The clinical application of sirolimus (SRL) as an immunosuppressive agent is largely hampered by its narrow therapeutic range. This study focused on developing SRL tablets with a sustained release profile for better safety. SRL was highly water insoluble and its solubility has been efficiently enhanced by preparing self-microemulsifying drug delivery system (SMEDDS). The SRL-SMEDDS was physical...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008